The rules are in StratOps. Fighters, Mechs, tanks with VDCs, whatever. And it doesn't matter if the launching ship is in space, in atmosphere, or sitting on the ground. The launch rate for your bays is two units per door assigned to that bay. A Kyushu has 2 doors assigned to the mech bay, so it can chuck four mechs per turn, period. By comparison, a Robinson has four doors on its mech bay, for a launch rate of eight mechs per turn, and an Overlord's six doors means twelve mechs per turn.
The only exception is when you're dropping/offloading/evicting infantry units, conventional or BA. Those have no door requirements, you can chuck as many as you want in a given turn.