How do I escape Fort Zancudo without getting wasted as Franklin?

Is there a way to get the minigun in Fort Zancudo as Franklin and escape Fort Zancudo without getting wasted?

I quick saved in the Fort Zancudo as Franklin.

There are a few ways to enter Fort Zancudo on GTA V story and none of them are easy. Because you're playing as Franklin I'd suggest trying to drive in. However, none of the gates open from the inside so you'll need to fly out. Drive to the mountain range to the north of the base and ascend the hills. There are ridges along the hills that are just wide enough to drive along. On the second hill from the west the ridge extends with a small divot which you can use as an improvised ramp into the military installation if you're travelling fast enough. Once landing inside the base drive as fast as you can to the ATC tower to fetch the minigun.

If driving is too risky landing a helicopter next to the tower may work too. However, soldiers armed with rockets are stationed on top of the aircraft hangars and may destroy the helicopter in flight or after you've landed. Your best bet is to parachute into Fort Zancudo and attempt to land as close the the minigun as possible. While you have almost no chance of escape you have a much higher chance to collect the weapon which you will keep, even if your character is killed.

If you are still keen on escaping, park your escape vehicle against the southern face of the tower so it's shielded from most incoming fire. If it's a helicopter ascend over the fence and then fly as low to the ground as possible. The terrain will help block incoming fire and may destroy pursuing jets which fly too close. If your escape vehicle is a car drive into the westernmost aircraft hangar and board the fighter jet inside. Once in the jet accelerate out of the hangar and pull back on the yoke as much as you can. With any luck you'll avoid incoming rockets and escape by flying inverted over the hangar the jet was just parked in. Attempting any other maneuver out of the fort using the fighter jet has a much lower chance of success. Once away from the Fort evade or shoot down any pursuing attackers.

My general suggestions are to bring the heaviest body armor you can find and save before making any attempts into the base. While the base is significantly more guarded on GTA story mode than multiplayer it may be worthwhile to make practice attempts in GTA Online before trying the real thing. Good luck.