You might post that question under Royal Star above if you don't get an answer here.
I don't believe you will have any trouble with wires being heavy enough. What you might find is something like needing a bigger fuse. I have not installed a trailer but I don't believe you will have this problem either.
Next thought might be the flashing rate of the flasher. I believe you can buy a relay at an auto parts store that is not dependent on the amount of current used to make heat and flash the turn signals. Take your stock flasher to the auto parts store they can cross it.
Lots of variables in wiring and capacity but generally, LEDs draw so little power that if your trailer only has LEDs you can pretty much add them right to the circuit without any concerns. Replacing incandescent bulbs with LEDs can make your flashers not work very well. Adding incandescent to your existing incandescent system will almost certainly overload your wiring and can do things from messing with your flashers to starting a fire.
The Royal Star threads will be your best bet for specific info & you should let them know exactly what kind of lights you have now and what kinds of lights you plan on having on your trailer.