Thwart does nothing to TAs. It ignores Feats.

Dissent however, allows you to counter TAs with Outwit as if they were powers.

Only TAs that keep powers from being countered (like PC or Quintessence) are immune to Dissent.

Thwarted? No - KC/HT is not a feat, so Thwart has no effect on it.
Dissented? Sure, unless some other effect stops you from Outwitting (Fortitude, Resistance, White Noise...)

I meant Dissent and Disbanded. I always get those mixed up.
That's what I get for asking a question without having the stuff in front of me.
I was just thinking maybe the "can't be ignored" would be referring to stuff like disbanded, but I can see how Phasing and Leap might react differently with KC than they would with Slippery.

Ah, I see. However, that still has no real bearing for two reasons.

One, the BFC is doing the ignoring, not the character trying to move.

Two, even if the wording of KC/Hypertime was such that it could be read to be immune from all effects that could possibly ignore it, BFCs have long been established to override pretty much everything in the game except core rules like the Rule of 3.

I'm just waiting for the feat/BFC/SP that explicitly states "this overrides the Rule of 3 and allows the value to be increased by more than 3 total" to show up.

Does the amount knocked back have to count out of your movement.

If I have a Flash with 14 movement Hypersonic and I try to base Iceman. Say I have moves 10 squares to get to him, and then the Slippery Roll hits and I get knocked back for 2.

Does this mean that I have actually moved 10 squares and still have 4 more I can move?

or

Have I now moved 12 squares and only have 2 left that I can move?

Knockback does not equal movement.
I'd say you still have 4 squares to go.