We recently purchased a house that was in a flood zone. We got a good deal on the house so I felt comfortable buying it even with that downside. I ran a check on FEMA's website (https://msc.fema.gov) which showed that a couple of my neighbors had gotten their flood zone revised. This meant our house had a good chance of success if we had a elevation certificate done. However, fair warning, I would not advise buying a house in a flood zone as flood insurance premiums are expected to increase even more in the future.
I will explain the steps I took in getting the flood insurance requirement removed from my property.
The first step is to order an elevation certificate from licensed land surveyors that basically tells you how high your house is. I would highly suggest calling a few companies as prices can vary greatly. One company I called wanted $700 to do the elevation certificate and another $700 to prepare a Letter of Map Amendment (LOMA). I went with a company that only charged an additional $150 to prepare the LOMA. I was told the LOMA was basically just some paperwork that the surveyor had to fill out for the Federal Emergency Management Agency (FEMA). All told I paid $850 to do the elevation certificate and LOMA.
The elevation certificate will tell you whether your house is high enough to be removed from the flood zone. If it is, then they can prepare a LOMA for you. It took FEMA about a month to process my documents. Once FEMA gives you the approval, I just had to submit a copy to my lender and flood insurance company and they took the requirement off my loan. In addition, I was told that because my flood zone was reclassified, I was eligible for a full refund of my flood insurance premium, even for the months I had already used.