Is it possible to install flush mount floor vents in a laminate wood floor?
I know I've seen stain grade wood grilles that could be flushed to the floor. I doubt they were 8mm, but you may be able to rout the subfloor to make up the difference or and/or bevel the grille edges. You would stain and finish to match, but you won't be able to perfectly match the stain. It's unlikely it's even the same wood specie. This wouldn't bother me, but would bother some.

Mind you, drop in vents usually have mechanisms to adjust direction and volume of air. Wood grilles are simply fixed slats of wood with no adjustment. They are also low on free area, which will diminish flow in comparison to similar sized metal vents. But they do look infinitely better.

For that matter, if you're handy, you could fabricate your own. If the least dimension isn't too wide, you could even use flooring. Either drill holes or rout slots, then paint the exposed edges. Just don't locate the leg of a heavy sofa right on the center of it.