Although this may sound like a strange request, it is what happens in the "Benefactor" mission of the vanilla campaign, and I suspect others too although I can't be bothered checking.
I am looking at whether I can make a "flashpoint" that is just a conversation as a workaround, although I can't terminate it without having the reward screen come up.
Once this flashpoint is complete, another will be generated that provides a follow-up conversation as you prepare to drop.
Kind of a sketchy work around, but what if you made the FP fail after the convo? I don't think failing one triggers a reward screen right? Make it add the tag you need before the convo ends, and also make the FP not spawn if that or some other convo granted tag is present. This would prevent it from reappearing once completed.