There are only a handful of places in the Navy that offer Chiropractic care (off the top of my head I know of Pensacola and via the Army at Madigan if you are stationed in the Seattle area). If there is a chiropractor on staff at the clinic (there very well may be) then they would have access. For what the mids need I'd much rather see a sports medicine or PM&R doc though.
Chiropractic care is not covered otherwise and as an active duty person you cannot be referred "into the civilian world" for chiropractic care.
I won't go into the debate as to allopathic vs osteopathic vs naturopathic vs chiropractic vs oriental vs homeopathic vs naturopathic vs quackery medicine and which of those fits as 'quackery' as it's never a fruitful discussion.