Yup, Kraft is not on Brady's side in this. Not a chance. The rights that the NFL is fighting to maintain are something that the NFLPA tried to get removed in 2011, but it was a non-starter for the NFL. Kraft was instrumental in bringing the two sides and getting a deal done. He was negotiating as part of the ownership that insisted that Goodell had to have this unchecked power.
In short, Kraft went to bat in 2011--left his wife's deathbed, by all accounts--to among other things ensure that Goodell would have the very powers that they're trying to keep in court. I'm fairly certain that Kraft wants the NFL to win this appeal, no matter how he feels about Brady personally or whether or not Brady "did it". Even if he's finally realized how unbelievably stupid it is to let Goodell have this kind of power, at a minimum he'll want it upheld so that they can get some concessions from the NFLPA in the next CBA negotiation in exchange for reining him in.
It's entirely labor vs. management at this point, and he's management.