Several good responses and advice here. (I'm a dance professor with background in kinesiology and exercise physiology used to teach childrens' dance classes and now teach students to teach children's dance classes). And yes, if your child CAN walk flat, he's OK. Just short--many adults wear heels and lifts to make themselves taller.
My concern is with his muscles, which can get tight from all that toe-walking, as well as the antagonist (opposite) muscle, the tibialis, not getting the work-out it needs to stay correspondingly strong. But I believe it's just short of criminal to subject a child to braces when massage and stretching daily will do the same job, is a good bonding experience for you both, helps him understand how to take care of his own body (not to mention cheaper!).
Find a time when he's quiet and relaxed--between bath and bed can be a good time. I won't go through a description of the massage/stretch unless you want it--they're soothing for you both, and my daughter enjoyed them when she was small; still does, and she's 12--so please feel free to respond and ask if you want them.
Best of luck,
L.