You can, but it doesn't work well. Meaning that Wranglers use a 3157 bulb and it is an extremely common bulb type, so they sell LED versions. However they hyperflash and the light pattern coming off them makes them dimmer in the OEM housing than the light pattern off a standard bulb.
In addition, what I was talking about in my first post is that it is impossible to replace the flasher in a wrangler. It is built into the circuit board in the dash. I looked into this in the past. The 2017 or 2018 may have a slightly different board as they could come with LED headlights as an option... However I doubt it.
One thing to know about the cheap LED lights you get from pretty much anywhere online (I have a set of cheap headlights so I'm not bashing them)
is that the reason they are cheap is the very limited shielding that gets put into them, in addition to the accuracy of resistance / voltage required, etc. It's the reason that the top names ones, along with any OEM are so ridiculously expensive.
With regards to what you are experiencing with the quick flash a few things come to mind as possibilities.
1. One of the reasons that standard bulbs seem to take longer to blink is because they fade in and out, where LEDs are almost instant on off. That could account for the very brief flash you are seeing.
2. I think the trailer connection is behind the left tail light.. and LEDs are strange. Because of their super low voltage requirement they can turn on or not turn on depending on how the little computer that controls them works. A standard bulb is nothing more than a resistor that glows, while an LED bulb is vastly more complicated. That trailer connection could be changing the voltage the smallest amount, but just enough to change how that sides LED functions.
3. An interesting test would be to temporarily switch the two rear lights and see if the same things happens. Obviously you wouldn't drive anywhere, but uninstall, then plug left into right and vice versa and watch to see what happens. It will at least eliminate either #2 or a strange malfunction in the light.
LEDs are strange.