I dealt with a cyano and dyno outbreak almost a year ago. Here were my steps on how I tackled them
1. Introduced Phytoplankton (Reef Nutrition Phyto Feast). Can easily be bought at your local fish store
2. Introduced Beneficial Bacteria ( Microbacter 7, Tim's Waste Away, and Vibrant). Bought on Bulk Reef Supply. Follow instructions on bottle closely.
3. Syphoned all the Cyano and Dinos every 2-3 days by attaching a filter sock @ the end of the siphon tube. The filter sock collected all the cyano/dino and was later soaked in a bucket with Vinegar then washed.