I would like to type Jan in A2 and AutoFill up to however far the selection
goes. However, there are some rows that are hidden. I am not able to autofill
the visible cells in the selection.

What I have done is:
Type Jan in A2
Select area to be filled
Select visible cells (by pressing F5 and clicking Special Cells)
EDIT | Fill | Series | Autofill

I get some weird results. Can anyone please help me get Jan, Feb etc with
only the visible cells filled so that there are no skipped months where there
are hidden rows.