Flood insurance rates, fees, etc are all controlled by NFIP. You cannot just add flood insurance, there's a process and that often includes getting an elevation certificate. Fees, rates ,etc can all change from year to year, and the rates are going up quickly to offset losses from huge flood events like this one. Thoroughly expect rates to jump up after Harvey.
I personally removed flood insurance from my rental house and got a Letter of Map Amendment (LOMA) to say my house was no longer in the floodplain so I wasn't required to carry the insurance from my mortgage. I previously already knew that my house wasn't in a floodplain, but the insurance was so cheap at the time that I went ahead and left it on for the peace of mind. My insurance went up overnight about $600/yr because it was a rental house and NFIP enacted a fee if you do not live in the residence being insured.
There are a lot of things that go along with getting flood insurance. For instance, if you actually are in a flood zone and you get flooded, you likely will not just be allowed to repair your home. You will have to improve your home (usually through elevation) so lowest finished floor is above the based flood elevation in the area. This can be hundreds of thousands of dollars, depending on the existing foundation, etc. Slab on Grade is the most expensive type of home to elevate as well.