Domesticating rats takes about 20-30 generations. Squirrels, though, take about 9 months to mature; rats are much faster, less than 2 months, which is probably one of many reasons why we've domesticated rats but not squirrels.
Still, hypothetically, it should be possible to domesticate squirrels within a few decades. In foxes, domestication only took 7 generations, so it could even be faster.
Incidentally, I have a new startup idea: first you domesticate squirrels, then you produce a line of commercially packaged squirrel food and an "invisible fence" type system for "outdoor" squirrels.