A good way of killing fleas and flea eggs on clothing is to throw the clothes in the washing machine and add some Dawn Dish Detergent to the laundry.
Then turn the washing machine on and let it run through a cycle and the fleas and flea eggs should be killed in the Dawn Dish Soap.
You can also wash your dog with the Dawn Dish Soap to kill fleas and flea eggs on the dog and then wash the dog using some Apple Cider Vinegar to balance it's PH level which the fleas hate so they won't be attracted to the dog.
When you dry the clothes on a high heat setting in the dryer the fleas will also die if there's any leftover fleas or flea eggs that survived the washing machine and Dawn Dish Soap.