Question: I was wondering whether the rotational speed of a discus has any influence on the flight of the discus. Would slowing the rotation or speeding it up change the trajectory in any way or would the flight simply become unstable when slowing down?

Answer: 
The faster it spins, the greater the aerodynamic side force on it; see [Magnus effect](https://en.wikipedia.org/wiki/Magnus_effect).

Also, higher rotation increases the $\mu$ (ratio of edge speed relative to body to airspeed of the body) of the disc; the higher airspeed of the advancing edge relative to the retreating edge creates asymmetric lift & drag. The former would impart a rolling moment, while the latter would impart a moment opposing the in-plane rotation of the discus.

All that said, I doubt either are particularly significant effects.
Given the physical conditions, this seems like an appropriate explanation: The faster the discus rotates, the more violently and quickly it displaces the air around it. Now the absence or scarcity of air causes a reduction in air friction or viscosity around the discus and this allows it to move onward in the direction of propulsion; now that depends on what angle the athlete projects it. After a certain distance there begins a constant deceleration of rotational speed because at some point, the air friction starts overpowering the rotation and this results in the discus entering the second half of its trajectory, i.e., moves downward along a curved path. I hope that answers your question.