Two of these are right: "I felt great watching the water flow swiftly." and "I felt great watching the water flowing swiftly."

If you like, we can take it a few steps further ... "I felt great as I watched the water flow/flowing swiftly." "I felt great watching the water. It flowed swiftly." "I felt great watching the water. It was flowing swiftly." "I watched the water, feeling great, as it flowed swiftly." "I watched the swiftly flowing water, feeling great." "Watching the water flow/flowing swiftly, I felt great." There are probably some rules about verb agreement somewhere in all these sentences, but at this point, you may be ready to throw yourself into the swiftly flowing water.