Will a flood insurance application along with verification of payment from the insurance agency suffice to close a loan located in a flood zone? Or is the actual policy required?

The guidelines say (when they were available) that you could close with a completed application and payment receipt.

From personal experience, I require my borrowers to also provide proof that the app and the premium payment have been sent in to the underwriting department since the agent must send everything in to underwriting within a certain number of days for the application effective date to be honored. In the past I have accepted only the app and payment receipt from the agent only to find that the agent left everything on his desk for several weeks before sending in to underwriting. When we finally received the dec pages for those policies, the effective dates were well after the closing date.