Is it a good idea when your child have atopic dermatitis he take swimming lessons?

It's a great idea: Swimming in a chlorinated pool may actually help his eczema, similar to the benefit of using bleach with bathwater. Be sure he rinses off after swimming (no soap, as it can dry the skin). If possible, let him air dry instead of vigorous rubbing with a towel. Apply liberal amounts of moisturizer when he's done (while skin's still moist). Talk with your allergist or dermatologist for info.

Wash off chlorine: The chlorine can greatly exacerbate the eczema. Try to wash all the chlorine off immediately after swimming. Don't use the harsh soaps provided at most public places. Bring your own shampoo and soap. Use mild gentle products without fragrance made for sensitive skin like aveeno, (oatmeal) cetaphil, cerave. Moisturizer after swimming and showering.