Where does Joseph fit into Egyptian History?
Is Joseph likely to have figured in Egyptian records?
If Joseph was placed second in charge of Egypt by Pharaoh, there should be some note of this in Egyptian records. 
If Joseph helped to save Egypt and the surrounding nations from a famine lasting seven years and acquired all the land of Egypt for the Pharaoh, he would have been a very prominent figure in Egyptian History. 
Joseph would have had to construct massive grain silos for storing grain in many Egyptian cities and indeed, massive silos can be found in many historical significant Egyptian cities today (eg Saqqara).
Joseph married the daugher of one of the High Priests in Egypt.  He saved his country from a seven year famine and bought up all the land of Egypt except for that of the priests who did not need to sell their land because Pharaoh supplied them with food. The people became loyal subjects of Pharaoh because of what Joseph had done.  Joseph was, therefore, responsible for making the Pharaoh’s wealthy and powerful. 
Joseph served the Pharaohs from the age of thirty.  He died at the age of 110 years of age and was given a Royal Egyptian burial. 
His family, the descendants of Jacob (Israel), produced mud bricks and became numerous in the 430 years that they lived in Egypt.
The pyramids of the 12th dynasty contained millions of mudbricks. Seven such pyramids were built over a 200 year period ending with those of Amenemhet III who also built an enormous mudbrick structure called the Labyrinth. A large slave labour force was needed to build the 12th dynasty pyramids. It is likely that the Hebrew slaves produced the bricks that went into the 12th dynasty pyramids. After the Exodus in the 13th dynasty, no more great pyramids were built.
There were over 600 thousand adult males (not counting women and children) who were led out of Egypt by Moses during a time of great disaster in Egypt. 
It is no wonder Joseph was given a Royal Egyptian burial and almost deified in Egyptian culture, having saved Egypt from a seven year famine, acquired all the land of Egypt for the Pharaoh, having been the first to construct buildings with columns, having designed the first pyramid, constructed grain silos to store grain, developed mummification techniques and taken the burial of Pharaohs to a new level by burying Netjerikhet in the first grain silo and constructing a pyramid on top of it. 
Where does Joseph fit into Egyptian History?
Estimates of dates have long been the common denominator used by archaeologists and historians alike when trying to piece together ancient history.
Various teams of archaeologist have used a number of different dating methods to estimate how old a particular artifact is. For example, the type of pottery that is predominant in a layer can be used to date the layer. As creationists have noted however, dating methods are highly unrealiable and cannot be trusted as authoritative, and certainly not where they contradict Scripture.
Assumptions behind various dating techniques are not alway right. This can sometimes lead to artifacts being incorrectly dated by as much as 1000 to 2000 years.
If history is pieced together based only upon the estimated dates of particular dynasties, the results can be quite erroneous and it will be little wonder why Egyptian and Hebrew history does not fit together and why no Egyptian equivalent of Joseph has been found using the dates traditionally ascribed to various Egyptian dynasties.
An increasing number of historians are now calling into question the dates of Egyptian dynasties. In particular, Sweeney , Velikovski , Fry   , Reilly  Down . They have proposed revisions of the Egyptian timeline which generally contract the Egyptian time frame and bring the dates of the Egyptian dynasties forwards. The revised Egyptian dates when aligned with the Biblical dates suggest new candidates for Biblical figures which now need to be confirmed by Character matching and Archaeological discoveries.
Using their revised dating systems, the historical records of Israel and Egypt fit together differently, purportedly making it possible to identify likely contemporaries of important Biblical Characters.
Conventional wisdom which has been very reliant on the Biblical record and timeframes, has been unable to find any evidence that the Patriarchs of Israel lived in Egypt and have not found any possible candidates for Joseph because they are looking for evidence of him in the Hyksos dynasty which is estimated to have been around 1700BC according to conventional chronology.
Many scholars have tried to place the Exodus in the 18th dynasty because of arguments related to when chariots were first introduced to Egypt. A lot of emphasis has been placed on this one point and seems to have sent many an archaeologist on a ‘wild goose chase’ looking for evidence of a mass exodus in the 18th dynasty (and of course they cannot find it because the Exodus took place in the 13th dynasty).
Although hundreds of Chariot Wheels containing 4, 6 and 8 spokes have been found in the Red Sea at Nuweiba by Wyatt and others, these chariot wheels had been dated to the 15th dynasty or later and so the 12th dynasty was overlooked. The fact that no 12th dynasty chariots have been found should not be surprising as the Bible tells us that Egypt lost all of it’s army and chariots to the Red Sea at the time of the Exodus.
Rather than looking for ‘Chariot Wheels’, we should be looking for lots of ‘mudbricks’ and what better place to look than the 12th dynasty. Mud bricks were used most prolifically in the 12th dynasty, not only for buildings like the Labyrinth, but also for the pyramids of the 12th dynasty.
A revised chronology results in a very different picture with the history Israel and Egypt purportedly matching better with “archaeological” records, which of course are subject to interpretation. Abraham is then considered to be a contemporary of Menes. Imhotep is considered to be the Joseph of the Bible and Djoser is considered to be the Pharaoh that he served   .
The revised chronology would fit with the theory that Amenemhet III was the Pharaoh of Moses who oppressed the Israelites making them make mud bricks . Also of note is that the pyramid of Amenemhet III was made of mud bricks containing straw.  Amenemhet III was the 6th Pharaoh of the 12th dynasty and lived 450 to 500 years after Pharaoh Djoser in the 3rd dynasty.  He had only daughters. One of his daughters Sobekneferu had an adopted son (Amenemhet IV) who disappeared before he could become King. It has been suggested that Amenemhet IV was Moses. 
If such is the case, the Exodus took place during the Reign of Neferhotep I during the 13th dynasty in 1445BC.  The Hyksos took over lower Egypt shortly after this with little resistance. The Hyksos reigned in Lower Egypt for around 400years. This coincides with the period of the Judges in the Promised Land. The Hyksos were finally defeated by Ahmoses who founded the 18th dynasty which was the beginning of the New Kingdom of Egypt. It would therefore follow that the Hyksos (15th & 16th dynasties) which were contemporary with Joshua and the Judges, came to an end when King Saul destroyed the Amalekites (Hyksos)  after they were forced to leave Egypt by Ahmose I who started the 18th dynasty (New Kingdom of Egypt).  This would place Dynasty 17 as contemporary with dynasty 16. Likewise the 18th dynasty as contemporary with the United Kingdom of Israel when Saul, David and Solomon were on the throne. This would also mean that Amenhotep I and Thutmosis I of the 18th dynasty were contemporaries of David.  Hatshepsut was the Queen of Sheba who visited Solomon.   Thutmosis III came to power during the reign of Jereboam and became the greatest Pharaoh of Egypt. 
The Biblical dates before the Exodus are determined by whether one assumes a long or a short sojourn of Israel in Egypt. This is another confounding factor that can throw out the Biblical dates by as much as 200 yrs resulting in an incorrect alignment for events prior to the Exodus.
‘Modern’ Chronology (Ashton & Down 2006) 
|Date||Egypt||Contemporary in Israel|
|2080BC||Menes (First Dynasty)||Abraham|
|1900BC||Djoser (Third Dynasty) + Imhotep||Joseph **|
|1531BC||Amenemhet III (6th Pharaoh 12th Dynasty)||Moses|
|1445BC||Neferhotep I (13th Dynasty)||The Exodus (Moses)|
|1405 -1021BC||Hyksos (15th & 16th Dynasty)||Joshua to Saul|
|1018BC||Amenhotep I & Thutmosis I (18th Dynasty)||King David|
|950BC||Hatshepsut (18th Dynasty) [Queen of Sheba]||Solomon|
|929BC||Thutmosis III (18th Dynasty)||Jereboam|
** Based on a 430yr long Sojourn of Israel in Egypt (Exodus 12:40)