Any thorough bath will drown some of the fleas. Flea shampoo really isn’t any more effective today than non-flea shampoo. Don’t waste your time unless your pet just needs a bath.
If you want the fleas dead, the university research veterinarians who study fleas recommend prescription oral products. CapStar, Comfortis, NexGuard, Bravecto, Simparica, Credelio. These are the safest and most effective way to kill fleas on your pets.