I may be completely wrong here so excuse me if I am. During my 20+ years of lugging a TV news camera around in the Aussie sunshine. A camera which cost me $35,000 plus a lens which cost $10,000, I suffered from flare. After getting caught with useless footage a few times I decided to run some tests to see if I could lessen the flare. After a few hours I figured it was something I'd have to live with, but did find a couple of tricks which didn't cure the problem, it just made it less of a problem.
I got some flat black stick on fine cotton sheet. Sorry, I can't recall who made it, but a friend's wife told me she used it in her hobby work. I cut out enough to stick around the inside of the lens sun shield (the conical rubber piece on the end of the lens) Plus I spent 30 minutes cleaning the lens glass with alcohol and one of those cleaning cloths the optometrist supplies with new glasses. Actually I think the cleaning did about 60% better than the stick on cotton.
As I said t didn't cure it entirely, but it did make it easier to live with. Obviously I kept the Sun at my back as much as possible and even used my wife as a portable sun screen. (don't tell he I said that)
According to out Prime Minister we were the only Husband and Wife news team in the entire world.
I realize your camera doesn't have a rubber glare shield, but I'm sure some Chinese manufacturer will design one soon, they always do. As for the cotton sheet, black paper or plastic can be reflective, but the cotton actually absorbs the light. If you can't find the adhesive type you can use the double sided adhesive tape instead. I purchased some only a few weeks ago and it was almost paper thin and would definitely do the job and I'd still use it on any after market Sun shield you buy in the near future.
Don't forget to give the lens a good cleaning to remove any oils, it's amazing how much it can mess with your recording. Good luck.