The trick to these Dynamo platforms is the timing. When you turn one on, don't turn the other one on in the middle of the jump. What do you want to do is turn the first one on, and jump on it. As soon as you land, turn on the next one, and jump on it. Keep doing the same thing, turn them on, jump on them, and remember to turn them on AS SOON as you land, or maybe even a little bit before. Don't turn them on too early, because they might deactivate too soon. Make sure you go fast enough, though. Oh, also, don't use a double jump if you can make it with a single jump, because double jumps slow you down.
I really hate the dynamo platforms in this game. I am playing my second time now in challenge mode and I was hoping they would leave out the dynamo platforms, but once again I am dealing with frustrations of the dynamo. I remember one room on my first playthrough that was dynamo torture, all they had to do was put a slingshot and it would take 5 seconds to get across, instead it took me several days of agony to get through.