I've got $5 riding on this. Here's some background, adding highlights to the relevant portions of the cards.
Raymond Flint: "Whenever the Corp takes a least 1 bad publicity, access 1 card from HQ."
The way I'm reading this, Raymond Flint does not work with Frame Job, because with Frame Job you're giving the corp a bad publicity. They're not taking it.
Flint doesn't say "Whenever the Corp takes or is given at least 1 bad publicity...." Frame Job does not say "If yo do, the Corp takes 1 bad publicity." I feel that the wording here is very deliberate, and therefore, these two cards do not combo.
English and grammar aside, I can explain it flavor-wise as well. When the Corp takes bad publicity, it's because they're doing legitimately shady things of their own volition. Flint, being a PI, would know that. But with Frame Job, the runner's the one doing something shady and pinning it on the Corp. Flint would recognize this bad pub as false.
Am I right? Or am I just being a tongue-clucking grammarian?