A “flat earth” is not physically possible in nature with real materials. Without the earth’s mass, you cannot keep the earth’s atmosphere. Gravity holds down the atmosphere, and the oceans.
Just assume for the sake of argument the BS that a flat earth’s solid components would not collapse into a ball by magic.
A flat earth would lose air and water.
Graphs of escape velocity against surface temperature of some Solar System objects showing which gases are retained. The objects are drawn to scale, and their data points are at the black dots in the middle.
With the earth being a funky flat disk the “escape velocity” is going to be tiny if the disk is thin and be large with a thick disk.
Your thought that the asteroid goes through the earth if disk implies you think it thin
I have no earthly idea how thick you think a “flat earth” would be other than thin as you imply the asteroid goes through.
I don’t know how to answer the question other than it is impossible.