There are no "private policies" for flood insurance. Other big insurers are attaching a flood insurance rider to such policies but the underwriter is FEMA. That is, a company like say State Farm sells you an homeowner's insurance policy and you add flood insurance. The flood insurance is underwritten--will be paid out on--by FEMA not State Farm, they are just the middleman.
Dumbass. I have a private flood insurance policy. It paid me a six-figure claim in 2013 and continues to cover me.