Thick. 4mm maybe? Thick, though. Takes a little time to break in.
I looked at those collab jackets again. If you can, try one on. They look a little long in the front (past your pants' belt buckle). Might not be too comfortable when you're hunched over the Thrux. You get that big mono-boob coming out of your chest.
The Lightning and a few others are made form the original '50s patterns, so they're very high-waisted, especially in the front (~1" above your belt buckle). That's great for riding. But may not suit your tastes when off of the bike.