Hey, I’m a chemist, and you’re getting some bad info from others in this thread.
Hydrogen peroxide decays into oxygen (and water) by itself over time, and certain things can speed that process up. What you’re seeing is oxygen bubbles that have been trapped by the soap.
Oxygen isn’t itself flammable, so trying to light those bubbles probably won’t do anything. You’d need to add some sort of fuel to the bubbles. I’ve seen hydrogen gas bubbled through soapy water and lit, and that is definitely exciting.
The mixture you’ve made is sort of on the way towards sodium percarbonate. You could get that more directly with some oxiclean (or a generic alternative). Probably won’t bubble because the peroxide is sort of locked up as part of the percarbonate, but it’ll still do its oxidizing thing. Oxidizing the chemicals that are a part of skunk odor makes them no longer smell.
Don’t use oxiclean or its equivalents on pets. Your best bet there is soap, water, and time.

