I did all new LED lights on my trailer. I have had no problems at all. My understanding, as mentioned above, is that it can depend on the tow vehicle. The LED lights have much less resistance than the incandescent types. If the tow vehicle has incandescent tail lights, then there is enough resistance already that it doesn't matter if the trailer's lights have very little. The tow vehicle's lights will have enough to function properly with the flasher.
If your tow vehicle was all LED, then you might not have enough resistance, and would get the rapid flashing or no flashing. So there you'd have to add the resistors in line or change the flasher unit in the tow vehicle.
I got my stuff from superbrightleds.com and have been very happy with them. I made new housings too, out of .040 6000 series aluminum. I wired mine up so that both reds on either side flash when making a turn. They are dual function so that half the LED's are for brake and the other half for running/turn. Works great.
See ya on the road,