so we have the application and the dec page of a private flood policy, the magic language ( “This policy meets the
definition of private flood insurance contained in 42 U.S.C. 4012a(b)(7) and the
corresponding regulation.”) is on the dec page.
Do we need wait for the actual policy or are we good to go?

My understanding is that the dec page is part of the policy. (I read it on the internet.)

FEMA's definition of "declarations page" says this: "The declarations page is a part of the flood insurance policy. (Found here: https://www.fema.gov/national-flood-insurance-program/definitions)

That said, I specifically submitted a question for the interagency webinar on private flood insurance as to whether the compliance aid listed on a dec page would be sufficient. They didn't directly answer this question, but said this in response to whether a dec page would provide enough information to determine whether a policy complies with the private flood insurance rules: A declarations page would not provide enough information for the mandatory acceptance rules or for the institution to determine that the policy meets the statutory definition of “private flood insurance.”