You need "with" between "be done" and a noun. In the sentence
I'm done with school.
"I'm done" means the same as "I'm finished" would mean.
But I don't think that's what you want in your sentence, am I right? I think you want to say,
Frank has done good work.
The meaning of this sentence is literal. The sentence
Frank is done with good work.
is grammatical, but it wouldn't make sense in the given context in my opinion.
Student or Learner