To find the time of flight, determine the time the projectile takes to reach maximum height. The time of flight is just double the maximum-height time.
Start with the equation:
vy = voy + ay t
At maximum height, vy = 0.
The time to reach maximum height is t1/2 = - voy / ay
Time of flight is t = 2t1/2 = - 2voy / ay
Plugging in voy = vo sin(q) and ay = -g, gives:
Time of flight is t = 2 vo sin(q) / g
where g = 9.8 m/s2
The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.