How many FACS sorted cells are needed for western blot?

It depends on your cell types and the protein you want to detect. Normally, we need 10e5 cells to do WB. But after cell sorting, cells we get at last (because of cell disruption or centrifuge loss) usually less than the the number shown in the cell sorter. So if is ok，the more cells you get, the better.

There is no simple answer for that.

It depends on cell type, depends on the amount of protein you wish to identify and the sensitivity of your western blot (e.g. how good is your antibody in detection and specificity).

What I suggest: do WB on a series of cell populations (e.g. 1000, 5k, 10k, 50k, 100k etc...) and see what is the minimum amount of cells you need for your specific protein.