How can quarks change flavors when they are elementary?

"Elementary" in this context means that they are not known to be made up of smaller particles. It doesn't mean they can't undergo changes. You can think of the flavors as different excitation states of the same particle - comparable to different vibration modes on the same string. In fact, according to string theory (which is not really a scientific theory yet - more a hypothesis), the fundamental structures in the Universe ARE a type of string, and the different vibration modes of those strings are what gives them their different properties.