Might be a dumb idea, but is it possible the use a Canon camera's internal flash as a video LED light (I mean continous lighting)?
Also, it is possible with ML?
I think you'll find that the bulb in your camera flash is not LED.
In addition, if you've ever had to wait for a flash to charge, and you hear that high pitched "wiiizzzzZZZZ",
it's because they require an amount of volts which far exceeds the batteries, so it charges up a capacitor to quickly discharge for the one shot.
https://en.wikipedia.org/wiki/Flash_%28photography%29
eBay and Amazon have many many very inexpensive LED video lights. Ring lights and all kinds of stuff.
Amazon ring lights (http://www.amazon.com/s/ref=sr_pg_2?fst=as%3Aoff&rh=n%3A172282%2Cn%3A502394%2Ck%3Aring+led+light&page=2&sort=relevancerank&keywords=ring+led+light&ie=UTF8&qid=1419831313)
Amazon DSLR LED lights (http://www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Dphoto&field-keywords=DSLR+LED+light&rh=i%3Aphoto%2Ck%3ADSLR+LED+light)
eBay ring lights (http://www.ebay.com/sch/i.html?_from=R40&_sacat=0&_nkw=led+ring+light&rt=nc&LH_BIN=1)
The camera's flash is a strobe, it is simply is not designed to output continuous light.