The Testimonium Flavianum is clearly questionable, no one accepts it as genuine, though the question of whence it came is interesting and ultimately IMO slightly strengthens the historicist case, but since it's clearly not a reliable passage it's not worth dwelling on.
The only really significant question is the account of James. He dismisses it because he has to, so claiming it's a forgery is another attempt to dismiss evidence. He's not a real philologist, it's great that he managed to get a peer reviewed journal to accept his work, but it's still a crank conspiracy theory attempting to wave away evidence. If denying evidence to prop up a conspiracy theory is your thing, then Carrier is great, but in truth all his work is weak and a waste of any serious person's time and you'd be better off dropping the conspiracies and fringe scholars and learning about the evidence objectively. The truth is more interesting than Carrier's conspiracies once you learn it.