Say the Runner has Flint in play, and the Corp scores Hostile Takeover (or Profiteering) for the win. Does the Runner have a chance to access HQ for a game-winning agenda, or does the game end first? It seems like the game ends first, since when the Runner scores vs Jinteki they win before Net Damage is applied.

On a related note, does Profiteering cause the Runner to access once or three times? It seems to me only once, since you take all the Bad Pub at the same time.

Just like the runner scoring the winning agenda off the top of a Jinteki Personal Evolution deck, the win is established as soon as the corp reaches 7 agenda points. this will not trigger any other events. (the runner accessing off Personal Evolution scores the agenda points before the damage is done, so cannot be flatlined by it.

Correct on both counts.