I tend to agree with Aragorn. The whole point of a chess board is that it's supposed to be square and the human eye is very good at picking out alignment errors.
If you decide to continue with the pieces that you've cut, you could try an old marquetry trick. Seal and sand the faces of the pieces individually. When you've got a satifactory finish, apply one more coat of sanding sealer and assemble all the pieces face down on a barely tacky surface. You can get temporary spray adhesives from stationers that do this; alternatively use adhesive tape that's been dabbed a few times to remove some of the stickiness.
Take some of the darker wood you've used and sand it to collect sawdust. Mix the sawdust with some glue to make a thick paste and force it into the cracks from the rear. Allow to dry, then sand the rear of the assembled board to give a flat surface. You need to do this or the board will never stick properly to the base material. Finally, glue in position and remove the tacky surface from the front of the board. Give it one final very light sanding - you'll find the sanding sealer will protect the light squares from the darker ones if you don't sand it too heavily. If you do, it's a case of reapplying sanding sealer and sanding again, repeating the process until no dark dust remains in the light wood.
I was hoping that someone else would have been able to make a better suggestion than this. It's a process that'll need a delicate touch and there's a considerable risk that someone who's inexperienced will get an unsatisfactory result.
Gill