FEMA is a bit confusing these days as the rules keep changing.
That being said...........
The only way to try to "improve" rates, if that's possible........... would be to have an "elevation survey" done ($500 - 900 here) and then apply to FEMA for what is called a LOMA (letter of map amendment).
If the home is in a designated flood zone - the lender will require insurance.
If you're paying cash, then whether you have insurance or not is up to you.
Your agent can check to see what type/level of flood zone the home is located in.... once you have that information - you can then call any insurance company that handles flood insurance for a quote .
You would have to check with FEMA and the latest flood maps. If you are designated in a flood area and you currently have a mortgage, most likely you would have to maintain flood insurance otherwise you would not be required to have it.
Hope this helps.
Jeff Hoover, REALTOR