Respectfully, I just wanted to say that I really, really dislike this idea. Enormously.
I don't believe this content is aimed primarily at people who nonsensically (story-wise) re-do story content again and again, I think it's aimed at people who don't, to focus them on content they can repeat and give them an incentive to actually repeat it. The reason people like this are in danger of falling out of the game? -> They have no interest in repeating story-heavy flashpoints.
I am assuming this a vanity grind to occupy people who are not running content like this because they have no interest in doing harder and harder modes of killing specific people they've already killed. Attatching this to flashpoints would just defeat the entire point. The people who are interested in repeating flashpoints already are.
Now you want to make some special new 'generic' "flashpoint" designed from a story point of view to be repeatable (maybe with a randomized boss name/appearance?) and attach it to that, sure, but I don't see that happening.
Remove all story element in NMM make the bosses harder, make everything harder, remove the option to skip packs and make the rewards worth the while and randomize loot so you wont get people all gunning for the same FP. Maybe make some minor twist or even better more FP