Yes you can use hydrogen peroxide in your Waterpik.
But you must dilute the hydrogen peroxide with some water before putting the hydrogen peroxide into the Waterpik.
The hydrogen peroxide will help to kill and get rid of any bacteria that could be in your mouth so your mouth and teeth will be much cleaner and healthier when you use hydrogen peroxide at least part of the time in your Waterpik.
I don't use hydrogen peroxide everyday or every time in my Waterpik but on some days I do and it cleans my teeth much better than plain water would.
Still you should use string floss often as well to keep your teeth all healthy and clean.