If you provide the part number and vendor for the LED's and for the turn signal switch, I will help you wire it up. I don't know about issues involving mixing LED and incandescent. I don't know how many flashers or what kind are necessary with mixed types. I can help you wire it according to the instructions. I believe you don't have a ground problem if hazard works and front turn signals work. So this points to LCD/turn signal switch miswire or flasher issue. If the front lights flash OK and the rear LED lights flash OK during hazard mode, it then seems that flasher is OK and that points to miswire.

So if I can study the parts you bought and instructions, I can verify wiring with you if you wish.

Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn