Toggle Flight Assist:
Hold Triangle, press R1.
In sum, Triangle plus R1. (in standard controls, of course)
Edit: it's quite possible to use it with a DS4 controller. You'll be easily using if for short periods while aligning to mail slots, dodging asteroids and chasing scum, after a bit of time. As for the long haul (playing strictly FA-off), I'm Kilo Lys away from that yet, but you'll probably need to customize your controller inputs, such as the XONE guys have been doing for quite some time. Like, throttle in the bumpers, Yaw on alternate input, Pitch and Roll in the right analog, Vertical thrusters in the left analog.