I dunno if what I did will work for you or not. There are a lot of war stories online and I tried a lot of things in isolation to no avail. I battled it for about 6 weeks... and am now dino free.
In isolation I tried:
- dosing hydrogen peroxide - by itself this made it much worse as regular nuisance algaes like cyano and hair algae will melt from h2o2 giving more space and nutrients for the dinos to flourish. Using something like chemiclean would be just as bad and I think this is a common mistake for those that are battling dinos and misdiagnosing them as cyano.
- stopping water changes - the idea here is that after water changes the dinos seem to flourish more so than usual. I can attest that this seemed to be the case as doing daily water changes as I was siphoning them out just seemed to intensify the problem.
- increasing nitrates - some folks online have noted that increasing nitrate levels to around 2ppm seemed to kill off the dinos. The theory was that they would burst from excessive nitrates. I tried dosing sodium nitrates for a week and really didn't see a difference.
- heavy manual extraction - I purchased some 50 micron filter socks, doubled them up and started siphoning them out into the filter sock that I placed in the sump. Thereby not doing any water changes. Make sure you stir up the water column as dormant dinos are all over the place and will look like near transparent strings... at least mine were. I even took a toothbrush to any coral or rock that seemed to have dinos established on them. This was painstaking work...
- reducing lights - I had the lights out for 4 days straight and when they came back on I only ran actinics for another week.
- removing sand bed - They would literally grow back to full strength so quickly and especially on the sand bed that I ended up just removing the entire sand bed.
- increased GFO - I doubled the amount of GFO thinking it was a nutrient issue... no avail. This unfortunately had a negative effect on my sps.
- introduced various different types of microfauna - this included different pods, mysid shrimp, mini brittle stars, asternid, and a bunch of different snail types.
Nothing by itself worked. So... there is no magic bullet here as far as I could tell. What finally seemed to work for me though was doing a bunch of these things together. First I spent around 4 hours doing the most thorough manual extraction I possibly could. Keep in mind that you can literally watch these things grow as you're removing them... so scrub or siphon out anything it's growing on... it was at this point that I removed the rest of the sandbed. After the manual extraction I went lights out for 4 days and dosed h2o2 every day at 1ml per 10 gallons. When the lights came back on I only used actinics for a week. During this time there were still a few dinos that would pop up. I would manually extract immediately... and then the most interesting thing started to happen... I got busy one day and told myself I would extract some of the few dino strands in the morning. Low and behold in the morning they were gone. Same thing happened the next day... and the next... until there were no more dino strands showing up at anytime. I think finding a natural predator for it would be the best solution... but none of the snails would really go for it and I'm not sure what eats these little protists. Everything has a natural predator though and something was consuming it. I'm not sure but I think it was some of the microfauna that I had added weeks and weeks before. It just may have taken time for them to grow to sufficient numbers and previously my outbreaks were so huge that they couldn't make a dent. I'm not really sure as I never witnessed anything munching on it but it was definitely at night when they would vanish mysteriously. As such, I think tanks with more diverse microfauna are more likely to never see this issue pop up.
Good luck, I'm hoping you have an easier time than I did.