Baby oil does not kill fleas on cats, but it may slow the insects down, making them easier to comb out of the cat's fur. Baby oil is thought to smother flea eggs, but this has not been scientifically proven.
The only way to prevent fleas from making a home in a cat's fur is to utilize a monthly flea treatment, usually applied topically. Such products are both safe and effective when used according to instructions. Some flea-killing home remedies may be harmful to cats, and a veterinarian should always be consulted prior to attempting any alternative treatments such as these remedies.