Water flowing continuously in toilet
That flapper needs to be replaced completely - good news! It's a very cheap part. 

Turn the water off to the toilet, remove the flapper, and take it with you to any home parts store of your choice. Pick a flapper of the same size (most universal will work). Once you get a new one in there - turn the water back on. 

With a new one it'll seal properly and stop flushing continuously.