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:
Well, there are definitely many, many more doctrines at play in this. For example:
However, those above are the "big ticket" items that are not necessarily common or are potentially debatable.
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.
To supplement the existing answer, perhaps the earliest Christian exposition on the idea of a 7000-year history corresponding to the seven days of the creation week is found in the Epistle of Barnabas, written in the early- to mid-second century AD.
In chapter 15, the author reinterprets the first six days of Genesis 1 as an allegory for six-thousand years of history (with the author believing he was living near the end of that sixth millennium).
He then anticipates these six 'days' to be followed by a seventh 'day' Sabbath rest, i.e. a thousand years of rest brought on by the second coming of Jesus:
At first the author seems to describe this seventh 'day' Sabbath as lasting forever, using ideas that typically are reserved for the new creation (e.g. describing this seventh millennium as the time 'when iniquity is no more and all things have been made new by the Lord'). Sticking strictly to the creation week of Genesis 1-2, this would seem appropriate. But then the author alters the formula by adding in an eighth millennium, basing the idea on Jesus' resurrection on the the 'eighth day' of the week (i.e. Sunday, the day after the seventh day Sabbath).
(Textually, there is no evidence Barnabas was relying on Revelation 20 in his anticipation of a future thousand-year rule of Jesus.)