The RAW is no, because you only have a Max of two fast actions per turn.
Knife fighter is for if you want more accuracy but lower base damage. Two attacks per round with d8 artifact die but only 1 damage.
Ambidextrous is for if you want to attack twice with more powerful weapons.
This should be the correct interpretation.
Ambidextrious, at least how it's worded in the swedish version, does not let you attack twice on one action. It let's you use your fast action to perform the second attack.
So since both ambidextrious and knife fighter only let's you use short actions for attacks, you are pretty much limited to only 2 attacks per round with this combination.
To compare, Sword fighter lets you do two attacks (Against different enemies) as part of the same action
. So if you had Sword fighter and ambidextrous, you could first attack two different enemies with your sword, and then perform a third attack (As your second action) against either one or even a third target.