I will assume that one or 2 leds will be on at the same times.
Your bluetooth device should be on the 3.3V. If it is the same that the one I got. Anyway serial is 3.3V on the PI so 3.3V it is.
I don't think that 2 AA batteries will be able to supply 1A for a long period. Even not sure it they will supply 1A. Don't forget if you step up from 3V to 5V, the power is the same and at 3V , the efficiency will be around 75% . The Input current should be roughly double on the battery side.
I suggest to opposite, use 6 batteries with a step down regulator. It will be more effective since battery could be a little bit discharge and still gives enough power.
A step down regulator like OKI-78SR, which will be around 90% efficient around 9V input voltage.
http://canada.newark.com/murata-power-s ... st=72R3616
I think your project is doable.
Ok let's be weird. What about using a pcb with pad like a keyboard. Each chess piece will have a metallic plate at the bottom
and will close contact (capacitive way). Maybe an old USB keyboard with the cpu stripped and the matrix reconnected to the chess board. This way you could just check the scan key to figure out which piece was lift and where it was put back on the chess board.