I did this once, but cutting small chess table squares individually is not easy even with a good saw, parts are so small, easy to screw up. I didn't put mine together yet but I'm using left over Brazilian cherry flooring & corian left over from another project.
Blade stiffening washers and a "good" fence is paramount.(Also a blade with more than 40 teeth, 60 maybe but 80 preferable )
I ripped 12" strips on table saw slightly larger then needed, then cut & squared ends on miter saw slightly larger then needed, recutting opposite end each time before sliding down to stop block to ensure ends were spot on. I then trimmed to final size on table saw. (Nibbled about 1/32" or less each pass). Yes its tedeous but patients will yeild a better result.
"You must become one with the wood grass hopper"