How long does it take for the approval of an allergy waiver?

"An allergy"? Do you mean "a waiver for an allergy"?

Nothing should ever take a year. That is incredibly too long. The longest I ever seen was 3 months and that was for a kid who was burned pretty bad as a baby and was in a burn center and had grafting done. His medical paperwork was like 300 pages. Bottomline, check with your recruiter. You need to be your own advocate. If you are not getting the answers you need, then talk to the SNCOIC. If need be perhaps you need to work with another recruiter. What is your allergy?