What is the basis for the idea of 7,000 years of human history, expressed by Larkin and others? Clarence Larkin projects a 7,000 year timeline of human history with each 1,000 years tied to a day of creation.  



What is the doctrinal or biblical basis for this theory?
Since you don't have any other answers at this point, I'll go ahead and throw out the ideas that I'm seeing play into this graph:


Young Earth Creationism

It would be hard to look at this chart written in 1919 and not start out with the realization that the author undeniably believes in Young Earth Creationism.

Young Earth Creationism is (essentially) the doctrine that states that the earth was (a) created and that it is (b) quite a young Earth (6,000 years old, or so).

See also: What is Young-Earth Creationism?
Anagogical interpretation of Genesis 1

This is a clearly less mainstream viewpoint.  The idea with anagogical interpretation is that we take events in the Bible and apply them towards eternity.

See also: What is anagogical interpretation and when should it be considered?

In this graph, Genesis 1 (the creation of the world in seven days) is being interpreted anagogically.  This interpretation is applying these seven days to seven millennia in human history.  (The six thousand years that Young Earth Creationism says the Earth has already seen and the millennium found in Revelations 21.)
Millennialism (compared to amillennialism)

This doctrine states that the one thousand years in Revelations 20 is a literal millennia (1,000 earthly years), rather than a metaphor or allusion to a time.
Dispensational Premillennialism

This is the idea that (1) Christians will be raptured (2) a seven year tribulation will occur (3) Jesus and the saints will return to Earth after the tribulation and (4) the literal one thousand year reign of Jesus on Earth will begin.  In that order and with those exact lengths of time.


Well, there are definitely many, many more doctrines at play in this.  For example:


Bible is the word of God and should be taken literally 
Revelations should be taken literally and all timeframes found in it are actual, earthly timeframes
Jesus was resurrected
Jesus ascended into heaven


et cetera.

However, those above are the "big ticket" items that are not necessarily common or are potentially debatable.

Closing thoughts

Many of these doctrines were popular at the turn of the 20th century and many are popular now as well. The one that stood out to me as somewhat surprising was the anagogical interpretation of Genesis 1.  Outside of that, this really seems to be a pretty straight-forward conglomeration of many prominent doctrines.