Every planetoid who gains gravity "normally" like Earth and Io and every other piece of matter in the universe gets it from their mass and radius. Escape velocity is also from mass and radius. My question is, how does escape velocity work if matter gains rotational gravity from its inertia, with negligible true gravity?
"Rotational gravity" is just false gravity emulated by centrifugal force. So, escape velocity would be either a) the inverse of the centrifugal force being generated or, (and much simpler) a corridor or tunnel to the outside of your ring/cylinder/sphere, where a craft would literally "fall" away at your rotational gravity pace (though it would stop accelerating the instant it left contact with the rotating body).
IOW: Escape velocity = "let go"
In the article, look at the basic diagram for rotational inertia, that would become your departing velocity the instant you were no longer bound to the rotating body.
It depends a lot on where you are going and the size of your ring
Let's say you are in a Nivan style ring world and you are trying to go out deeper into space. The most practical approach to escape velocity may be to just open a hole in the floor. Then you just need to time your escape such that you go flying off in the right direction effectively "falling" to your destination.
Now, let's say there is somewhere you want to go inside of the ring and you want to know how fast you need to go to reach zero apparent Gs, the answer lies in matching the Tangent Velocity of the ring by moving against its rotation. Once you reach the Tangent Velocity relative to the ring's surface, you will become stationary in space and no longer under the influence of any artificial gravity. At that point you can fly off at whatever speed you desire unaffected by the ring's rotation.
Larger rings require a higher Tangent Velocity than smaller rings to achieve the same apparent gravity. As you can see demonstrated in this trajectory calculator I wrote for L. Dutch's previous previous question about rotational gravity physics, you see that a Nivian Ring world rotates at over 1 million m/s whereas a Stanford torus only rotates at 94 m/s despite both having the same apparent gravity.
Just use the attached calculator and you can find the "escape velocity" of any ring by calculating for the tangent velocity.
Side-note: don't accelerate with the direction of rotation, that will actually increase your apparent gravity.