Rocket is for poking, chasing, hitting snared targets, team fighting, wave pushing or to get a few quick hits before the enemy is in Machine Gun range.
Machine Gun is for straight DPS, turret taking, dueling and cleaning up (Once you trigger your passive).
Jinx's mediocre Attack Speed makes her Rocket a poor choice for DPS, despite the awesome bonus. Most of the ADC's damage comes from crits over small periods of time, rather than straight up big damage.
The stacks will instantly disapear when Jinx autos with her Rockets once, which is why she tends to stick to Pow-Pow during longer fights. I assume the reason for that is because Riot didnt want her to enjoy both bonuses at once, even if for just a few seconds, and frankly, i agree with that decision.