The more this advantage is the flea because it can harm the dog

Think about it for a while.

Which of the two is happy to be together with the other?
Is the flea happy to suck the blood of the dog?
Or is the dog happy that the flea sucks its blood?

Unknown asks a good question. But of course, when the dog bites the flea, the results are more dramatic than when the flea bites the dog.

EDIT: I assume this is really a question about whether either animal is a parasite (vs a commensal or symbiont) and if so which one is the parasite.