DNA is a molecule, present in the cells of your body, that encodes genetic material. I'm sure Disney would be quite happy if your brother kept his DNA -- including his hair, skin and bodily fluids -- to himself.
Fingerprints are just that -- a print of the skin patterns on your finger.
Unless Disney is scraping cells off of our finger, it doesn't have your DNA. It has your fingerprint. If you ever apply for any kind of job in teaching, childcare, law enforcement, etc., you'll have to have your fingerprints taken. Your parents may have even had them taken as a child in case you ever got lost or kidnapped.
There is no evidence that Disney retains anyone's fingerprint, nor is there any conceivable reason why they would want that information. If your brother is that concerned, he can simply burn or scrape off the top layers of skin on his "scanning finger" every time he visits Disney World, being careful not to spill blood and skin (which will contain his DNA) on Disney property. This is the same practice many Nazis engaged in after WWII, to evade identification if they were ever captured (or wanted to attend a theme park). The procedure will be excruciatingly painful and he'll have to allow a few weeks in between visits so the finger can heal, but we all know that a trip down Splash Mountain is worth some sacrifice.
