flak vs. criticism

No, it doesn't fit as a straighforward synonym of criticism.

noun INFORMAL
strong criticism or opposition:
She took/caught some flak from her parents about her new dress.

It is used in an uncountable way - as in the example above - so we usually talk of some flak.

Also, its use in this way is metaphorical from the original meaning:

flak (FIRING OF GUNS)   Show phonetics
noun (ALSO flack)
the firing of guns from the ground at enemy aircraft, or the things that the guns fire:
They flew into heavy flak over the target area.

so we use it in the sense of someone being verbally 'attacked'. Merely having a criticism of something isn't the same.

I gave Peter a lot of flak about his new concept, and it probably wasn't all deserved, but my one major criticism of his proposal is...