I'm installing a pergo product over a vinyl kitchen floor, do I need to remove the vinyl to the wood sub-floor? Or can I install right on to the vinyl? Also do I have to use an underlayment since the kitchen is over the basement, no sound or moisture issues? I have been advised by both ways on this and would like a clarification.
Thanks

You probably will get both advices here too :-).
My advice is that you should use an underlayment - to dampen the noise when you walk over the laminate.
If the vinyl is in relative good shape, it probably will do the job. This way you win 2 times: no work to remove the vinyl, and no new underlayment to install.
Also, if there are no instructions included with the laminate, the vendor of it normally is best qualified to give you good advice.