You may not be a subordinate lien holder on the building subject to the language of your DOT.
No, you can not close the loan until all buildings in the SFHA have flood insurance. Also don't forget to provide and obtain acknowledgment of the Notice of Special Flood Hazard and Availability of Federal Disaster Relief Assistance in timely manner before closing the loan.
Doesn't matter what the other lender did. You are the one processing a new loan and the requirements fall on you to make sure the proper amount of flood insurance is in place. Either through verifying the other lender has a policy in place or you obtaining one. See page 27 of the MPFIG for the minimum coverage requirements. Notice it says loan(s).
The opinions expressed are mine and they are not to be taken as legal advice.