On a Kickr, 10 sp with 135 spacing should work just fine. They are designed to accept it with the supplied adapters. There is a supplied 1.8mm spacer that should go on the inside of the cassette against the trainer that is needed for 10sp. For 11sp you don't need that as the extra cog takes its place. Since this bike is not going to be used with wheels you can then adjust your derailleur to mate up with the first cog and adjust from there. I'm assuming you are using Shimano too, if you are using Campy, I can explain that as well but it is a lot more complicated. In my case I have Campy 10 and it has to work with wheels and trainer and the first cog must be in the same spot relative to the dropout on both unless you are willing to adjust the derailleur each time you swap. That is a big PITA if you ask me.
If you hub is a simple loose ball bearing hub...in 130mm, just replace with a 135mm (145mm axle) and add a 5mm spacer to the non drive side. Keep the right side the same.
There is no hub. Just a cassette on a freehub on the trainer itself. No wheels.