New LED Recessed 120V lights constantly burning out

I installed a ceiling fan in my living room with a harbor breeze wall control. I have recessed lighting in my living room with 5 lights. I replaced the center light with the ceiling fan and, yes, it is re-enforced to hold the weight of the fan. The wall control has an on/off switch and 5 buttons: 3 fan speeds, one fan off, and a light button that controls the lights on the fan. When I turn on the switch, all the recessed lights come on, but not the fan light. The wall control works like it should for the fan, but in order for me to use the fan lights or fan, all the recessed lights are on full brightness. The bulbs are dimmable in the fan and recessed lights. I would like to be able to dim all the lights with the same control. If this is not possible, I need help installing a new switch to control the 4 remaining recessed lights. Any help is greatly appreciated. Thank you in advance!

I installed a new 6 bulb LED fixture where an old 2 bulb incandescent fixture was. The bulbs are the Edison style bulbs and are definitely dimmable. When the switch is all the way up on the brightest setting, the bulbs flicker - only when other outlets are drawing power. They never flicker when on a lower setting (maybe 2/3 brightness). The confusing part is that the new fixture should be drawing less power in theory and also, it doesn't matter where I plug in a little handheld vacuum, they flicker. Even in a different room that's on a completely different circuit. I already pulled the light down and re-tightened all of the connections. I don't have a ground wire coming from the junction box - just a hot & neutral...could it have anything to do with the way this fixture is grounded? Any initial thoughts? Thanks!