I have a 6mm Rem Improved, 24 inch barrel. If I rechambered it to 6XC, and idea how much barrel length I would lose?

Look at the cartridge diagrams and then subtract one thread width. I did this and got 0.116 + .003 = 0.119

Your smith may want a 0.004 crush fit so call it 0.120". This is based on shoulder length I did not check the overall length difference.

Went back and checked the OAL and it is the determining factor the 6XC is 0.604" shorter than the 6AI. 2.055 vs 1.911".