If I am fostering a kitten and it is full of fleas, I always give it a warm bath with Dawn dishwashing soap well rubbed and bubbly into its fur. It has to stay under water for at least five or more minutes, (not the head, lol,) and the fleas will make their way to the head and then you pick them off and drop them into water set aside in a cup where they drown.
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This works 100%. Fill a small tin with luke warm water. Place the kitten in and keep the head above water! Get the kitten completely wet and hold it in the water for about 20-30 seconds. The fleas drown. Then just comb them off. Bathe them every other day. It will also get them used to being bathed.