Vinyl or silicon

Would you recommend a silicon or vinyl chess board ?

Neither. Option C: “flex” by chesshouse.com

Yes! The Flex pad from Chess House! I have one and love it.
There are other places that have the thin mousepad rubber. (Is it neoprene?) Whatever it is made of, it is a good compromise between vinyl and silicone.  Vinyl doesn't always lay real flat, but it cleans easy by just wipeing  it off, and pieces slide easy.  Silicone cleans easy by washing it,  but it attracts dust and other debris due to its tacky nature. Silicone, also prevents the sliding of pieces and can tear up real felt base pads on pieces that have them.  However, it folds up small and retains it's shape to lay flat.   Fex pads on the other hand, lay flat and fold up almost as well as silicone, and  allow pieces to slide adequately though not as well as vinyl but much better than silicone.  The trade off is that they so don't clean as easily as vinyl and silicone. 
ACE even has some printed with wood grain patterns that look real awesome. 

They’re so cheap that you can afford to replace them when needed. 

Thanks for the suggestions , I'm going with the flex.

Does folding it makes crease like in Vinyl? Or is it crease free like Silicone?

It does not crease regardless of how you fold the Flex board. Think of it as a thinner mousepad chessboard. Less bulky. More color options and Brighter colors because the texture is less fibrous than the old mousepad style. 

Neither - solid wood always, and not that veneer stuff . . .

Anyone where can I find a vinyl chess mat with triple weighted pieces of this style?

That appears to be a photo from the A&A Tournament Chess Set (see this Amazon link). The pieces are quadruple weighted and the set comes with a silicone mat. If you really want a vinyl mat to use with the set, you can separately buy a 20"x20" vinyl mat (see this Amazon link).

Thanks, appreciate it.