I can't remove the canopy on a flush mount fan. It turns a little but it will not slide out"

Typically there are 4 screws on a flush mount. Can you see them? Did you remove them? If it is a 4 screw mount, you need to remove the two that are not in the slotted part. Those in the slotted part can be loosened. You did remove the blades didn't you?

In addition, Most always, Remove Light kit, Remove Blades, then the screws, Rarely you may find one where you press in a spring loaded button/nub, then lift over opposing nubs on other side.