Does FHA allow a refund of the UFMIP if I refinance to a conventional loan?

No. The Upfront Mortgage Insurance Premium (UFMIP) is not refundable, except in connection with the refinancing to a new FHA-insured mortgage. 

To find out if you are due a refund search HUD’s database at http://www.hud.gov/offices/hsg/comp/refunds/index.cfm or call (800) 697-6967.