The little elecrtronic flasher that came in my old junked ScootNGo worked with the homemade LED turn signals I used on DayGlo Avenger. Those only drew a little over 100mA, IIRC (it's been at least 3 years, so...you'd have to verify that on my Electricle blog).
I expect a replacement can be had from the cheap scooter replacement parts websites, of which there are several. It runs on 12V, and has only two connections, positive and negative, like the old thermal flashers.
If I knew where it was at, I would get some pics so someone coudl reverse-engineer a schematic for it, in case anyone wanted to build a copy. But there are a number of circuits that will do what it does, easy to build even without a PCB, and can easily be found with a web search.