Your child will benefit from lessons in alliteration because, by learning to identify and pay close attention to the sounds in words, they'll be able to discern how different words vary in their pronunciation. Also, alliteration helps children think about reading in a different way -- they will pay closer attention to the sounds that certain letters make when grouped together, and this will help them sound out difficult words and, eventually, become faster readers.
When you're driving, look out to what is within your view and shout-out a color. Ask your child to come up with a person, place or thing that has the same beginning sound as that color. For example, if you are at a red light, yell out red. Your child should say something like "red robin" or "red rose." Allow your child's imagination to go wild with this exercise and let them make up any combination of words as long as they use alliteration.
This is another activity that can be done while in the car. You will work with your child to come up with the name's of people he knows. A great way to start off and get them excited is to begin with their own name, then your name, his sibling's names, etc. Once you've got a name, ask your child to come up with as many words as he can that use alliteration with the name of the person you've chosen. For example, if your name is Cindy, your child can say words like "scissors, sand, super, and soil."
If your child likes animals, this will be a great way to sneak in learning while having fun. Ask your child to come up with an animal and then to name the animal using a name that has the same beginning sound. Do the first exercise yourself to show them the way by saying, "I have a horse name Harry. Harry the Horse." Don't worry about going in alphabetical order, but try to cover as many different letters of the alphabet as you can think of.