Kyle Katarn not gaining appropriate TM?

Against who?

There are some characters that prevent TM-gains in various situations. Most likely you faced Hux on the enemy team; he will prevent all bonus TM while he has advantage.
Other explanations could be that you somehow included Padmé in your squad?

JKR lead also prevents opponents from gaining TM before the first turn of the game, iirc…

No, that just says from Leader abilities.

What was the opposing team?

It was in LSTB in the first wave.