It's not the flasher causing the problem, it's the fact the TJ's turn signals and side marker circuits were designed with conventional incandescent bulbs in mind. Incandescent bulbs conduct equally in both directions, LED bulbs only conduct in one direction so they disrupt circuits that depend on the bulbs being able to conduct in both directions. Like the current flow through them reverses when the headlights are turned on.
Personally I only run LED headlights and tail lights without problem. My side markers are LED and they don't work right when my headlights are on. I so seldom drive my TJ at night that I never bothered to alter their circuit with a rectifier to fix the problem.
Essentially I'm saying that LED bulbs won't always work right in our TJs, don't expect them to.