If the Earth is flat, does that mean we can put engines on it and fly it around space like a big dumb Frisbee?

No; you would annoy the elephants...

If the Earth was flat, cats would’ve knocked everything off the edge by now.

If you mean that you assume the earth is a cube, then maybe a rocket or a satellite be launched. There may exists an escape velocity, but may not 11.2 km/s. (Just for your reference)

no

You can't do that

Earth is not flat like the Bible teach.

Maybe

Proof that earth is flat but still spinning:

It's a fidget spinner

No. There earth is the center of the universe and the stars are just little pin pricks of light on the surface of the dome that covers the earth. So there is "outer space" to fly through. (Somebody was sleeping in their science classes or they would have know that.)

no