My minor battle with Dino's lasted around three months according to my notes, possibly longer since I didn't know what i was dealing with at first. It coincided with adding a skimmer to my system which caused all the hair algae I had to die back, making room for the Dino's to move in. Not sure if the sudden drop in organics was the cause in my case or what.
After extensive reading my plan of attack was to stop water changes unless absolutely needed. Water changes seemed to fuel growth based upon my observations and the opinions of those online who I read about. I also backed off on skimming to dirty the tank and get back some competing algae. I maintained alk, ca, mg through additives.
In addition to stopping water changes the thing that really seemed to beat them back was siphoning out the Dino's. For about a month I siphoned out the Dino's through a five micro filter sock and into a five gallon bucket. I then took the water in the bucket and passed it through the filter sock again when adding it back to the tank. This allowed me to keep water volume without adding new salt water to the tank which seems to contain some mystery trace element that fuels Dino growth.
After doing the filtering, daily for around a month they just seemed to slowly vanish. I then did a water change and held my breath waiting for them to come back, luckily they didn't.
Not gonna lie in my case it was a pain in the a** dealing with them, even though my case was minor. Siphoning them out only to have patches form again in a matter of minutes, and this happening for days on end, it was disheartening. You just have to be very persistent and patient and when you overcome them it will be very gratifying to have your reef back.
This is all based on my experience and for all I know it could of been for some other unknown factor that led to their demise haha.