Will carpet cleaning kill fleas
Yes and no, although the high heat will often kill adult fleas, juvenile fleas and eggs are less likely to be eradicated by steam cleaning alone.
A 3% hydrogen peroxide also has the ability to act as an insecticide and a lot of cleaners do use this when they conduct a clean, but the best course of action is to contact a licensed pest controller if the infestation is large, or it is for an end of lease obligation.