Can hydrogen peroxide kill fleas on dogs?

Not particularly, hydrogen peroxide is fairly harmless at the common 3% concentration. It is used for inducing vomiting in dogs that have ingested poison. Pour it down the dog's throat and up it comes. It works on people, too. It might not be a good idea to use it on rats because they don't vomit. Some people use it for mouthwash. It doesn't taste very good so you shouldn't need to worry about your pet drinking it.

Higher concentrations of hydrogen peroxide, up around 30% or higher become dangerous by being a good oxidizing agent. Explosive decomposition could occur if a catalyst is introduced.

To get a feel for that, take a half cup of 3% peroxide, mix a few drops of dishwashing liquid then sprinkle some dry baking yeast into it...do it outside. The gas making the foam is oxygen.