Key signature is the group of sharps or flats to the right of the clef on a staff.
Tablature does not have a key signature.
If you flat the A minor pentatonic, it becomes a G# minor pentatonic, not Ab minor.
The G# minor is relative to the B major, Check it out on your circle of fifths.
Now if you play the G# minor pentatonic, the positions do change. Because what you were playing in 5th position before, now you play it in 4th position.
To writte the G# minor pentatonic scale on tablature, just writte the A minor pentatonic, one fret lower.
Here is the G# minor pentatonic scale:
[G#-B-C#-D#-F#]

e--------------------------------------------4---
B------------------------------------4---7-
G---------------------------4---6-----
D-------------------4---6-------------
A-----------4---6---------------------
E---4---7-----------------------------

So now you are playing in 4th position.