Years back I installed a GFI outlet in a bedroom that was wired in K&T. Every time I turned on the hallway 3-way, the GFI tripped. Has anyone ever had a problem with GFI's and K & T? After that I now install non-gounding outlets on K & T.

I bet you have a short to ground on a neutral. That could have gone on unnoticed forever. It could also be high resistance ground on a hot (petrified mouse or something.

I put gfi protection on K&T fairly often.

My guess would be that the far end of that three-way circuit (light fixture) is getting it's neutral from something other than the GFI's LOAD neutral output.

Basically, your hot LOAD output is feeding the point wire of the 3-way switch at one end, and the point wire at the other end is feeding the fixture. Problem is that the fixture is getting it's neutral elsewhere, even if it is on the same circuit ahead of the GFI.

Do you need to have the GFI protecting the circuit downstream form the device itself? It's a bit odd for K&T circuits to loop from device to device, but this does happen. Why not just put the in and out wiring on just the LINE terminals and be done with it?

This happened to me years ago. There was only one hot and one neutral in the box that I installed the GFI in.