Our findings indicate that premiums as a percentage of coverage purchased are regressive: premium shares are larger than income shares for lower-income zip codes. Payouts, however, also as a percentage of coverage purchased, are progressive, meaning lower-income zip codes receive a larger portion of claims paid. Overall net premiums (premiums – payouts) divided by coverage are also regressive.
That is from a recent paper by Bin, Bishop, and Kousky, via the excellent Kevin Lewis. Here is Politico on the fight to thwart flood insurance reform.