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I would say that it should take around 30 days for the FHA streamline refinance. Since you have all your information together from the last lender you should be able to easily give that information to another lender if you wish to do so. [self promotion deleted by Zillow moderator.
You can also consider the traditional refinancing breakeven formula: how long will it take you to recoup the money you spend, assuming your monthly payment decreases (divide the monthly savings by your total closing costs to figure out how many months this will take).