A one-month-old kitten with fleas can be treated by disinfecting the environment, bathing frequently, deworming regularly, and minimizing contact with the external environment.
If a one-month-old kitten has fleas, the first thing to do is to isolate the kitten to prevent it from infecting other cats or humans. Then, the home environment should be disinfected. 
You can give your cat a medicated bath and regularly treat it for external parasites to prevent the growth of external parasites. At the same time, limit your cat's contact with the external environment and keep it away from grassy areas to avoid parasite infection. Clean your cat promptly after returning from outside.
Medication can also be used. For kittens with fleas, external parasite medications containing ingredients such as imidacloprid or selamectin can be used. First, kittens need regular external parasite prevention treatments. If fleas have already appeared on the kitten, the medication can be used again within the safe limits; it is recommended to consult a veterinarian promptly. In addition to treating the kitten for external parasites, it is also necessary to disinfect and clean the kitten's living environment and belongings.