LED conversion, 1971 Scamp

None of the answers I read above (or might have missed something) address the symptom----"all 4 flash"

THE FIRST THING WE NEED TO KNOW is what are we working on? Year/ make model?

You may have a problem in the hazard flasher switch or "left it engaged."

You may have a bad/ wrong bulb in spite of "what you think" or

One or more of the bulbs may not be properly indexing in the socket AND INTERCONNECTING the two contacts in the socket, thus interconnecting the tail and signal circuits

The last possibility is the standard answer---one or more of your sockets may not be grounding, OR the LED's may not "for some reason" be actually grounding in the shell of the socket(s)

What I'd try.......replace the LEDs one at a time with regular bulbs, perhaps 1 then both rear, then put the LEDs back in if that shows no symptom, and then maybe 1, then both fronts, and maybe 1 front and 1 rear, etc

Another thing you might do is get some alligator jumper leads and check all the LEDs to make certain they actually operate correctly. If you are unaware, 1 of the contacts to the shell is the "weaker" tail or park light, and the remaining contact to the shell is the brighter signal / stop light. With an incandescant lamp, you can LOOK and see which filament is working. Not sure how'd you do that with an LED

NEVER assume something is "good" even if you bought it new