A343 (cont.) I will again cite relevant rules in the spoiler. However, I would invite you to open a new thread if you wish to discuss this further, as I feel this is no longer a "Simple" RAW question.

Spoiler: Iaijutsu Focus and Knowledge Devotion
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Quote Originally Posted by IF
OA p58.
Check: If you attack a flat-footed opponent immediately after drawing a melee weapon, you can deal extra damage based upon the result of an Iaijutsu Focus check. ... the winner accumulates extra dice damage according to the accompanying table.
Iaijutsu Focus provides extra damage, it is not a modifier to the damage roll, and so would NOT be multiplied on a critical hit. On contrast...

Quote Originally Posted by KD
Complete Champion p60.
You then receive an insight bonus on attack rolls and damage rolls against that creature type for the remainder of the combat.
Knowledge Devotion provides a static bonus to the damage rolls based on the check, and so WOULD be multiplied on a critical hit.