I was pulling a trailer and the lights started blinking and then i notice that my rear running lights and dash lights went

BCM shorted out when your wiring shorted

Quite often it is in your trailer plug, but you have a damaged wire somewhere, First check your trailer plug, replace fuse if it blows now then unplug the plug under the dash on the drivers side pillar that runs under the carpet, replace fuse if it blows now you will need a professional, if it works you know where to chase it

Failed Battery is where I would start my testing

i don't know why but dodge trucks back feed threw the trailer lights and leave light on

There are separate fuses in the fuse box for the trailer lights than for the vehicle lights. Ensure these fuses are good. The trailer lights work without any special settings on the vehicle light switch.
If you're getting no lights whatsoever (no brake, turn, or running) then you likely have a grounding issue. This is usually the white wire on the trailer lights.

Do you have a 7-wire, 6-wire, 5-wire, or 4-wire trailer light connector on the rear of your vehicle?

you are going to have to get under it and start looking for ripped wires or damaged wires. also check around your trailer hook ups. dont know what type of ditch you hit or how you went in or how it was pulled out. if you went through some sapling trees or brush you could have torn up wires. if you blew a fuse then you had to short out wires. if tail went in first then trailer connector is a good place to start.

I presume you have your head lights on when you are checking the running lights ...

Replace the burned out license plate light

does every work properly with the wiring to the trialer disconnected? (un hook the wiring to trailer and put back the way it was) and let me know

if there is trailer wiring at the rear I would check there first, you have a short somewhere. or incorrect bulb, did this just start or has anyone looked at this?

exactly what does it do? please explain what happens when you press the brake turn on the light than brake signals ect.....