You can use johnson & johnson baby shampoo. Just apply it and gently rub from tail to head then let it stay for 2 to 5 minutes. After this comb out with flea comb then bath as usual. If it doesn't work you can use white distilled vinegar made from grain (MIZKAN - brand of the vinegar) is one of japan production. Just spray undiluted vinegar directly on the puppy and be careful for the eyes and nose then gently rub forward and let it stay for 3 to 5 minutes then rinse with warm water. After this bathe as usual using puppy's shampoo.
I once used teatree oil mixed with water to help a two week old flea ridden abandoned kitten with great success. I would be reluctant to use commercial products at such a young age.
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