A washing machine will kill flea eggs and fleas on clothing as long as you use hot water a good detergent and if your washing machine is equipped with the "turbulence cycle" set the washing machine to turbulence cycle for best results if possible.
You could also wash your clothes in some flea shampoo first and that will certainly kill the fleas and flea eggs and then wash the clothing again using your regular laundry detergent.
Or mix some flea shampoo with the regular laundry detergent so that the fleas will certainly be killed during the wash cycle.