I read in a book that red birth marks disappear by age 6?

Depends. Some do some don't.The pattern they take varies with the type of "red" birthmark and there are several.Some actually persist through lifetime.
Usually. Red marks such as capillary hemangiomas tend to disappear about the time the child is ready to go to school. Unless the red lesion is causing some serious problem, it is probably best to wait until that time before doing any treatment.