It would certainly be impossible for anything more than maybe 1/8" and even that is likely to result in just a lot of cracked pieces.
To get a small piece of 1/8" thick kevazinga like the one shown, you COULD cut a bubinga log to a short length and then make two circular cuts 1/8" apart and then soak the hell out of the piece and weight it down flat and then pray (probably without success) that it doesn't crack when you take the weight off (or even as you put the weight ON).
EDIT: Because bubinga is SUCH a big tree, I guess it might be possible to make rotary cutting on the outer part work at 1/8 but it would require some kind of wetting and I don't think you could get it soaked fast enough, so probably still just end up with lots of cracked pieces.
2nd EDIT: and by the way, "veneer" processing would NEVER Be used for something as thick as 1". That's what saw mills are for. The veneering process would just crack the wood.