If your basement get really damp and you know you live in a flood zone, you can still finish the basement and be smart about it. You can prepare the space properly and use materials that aren't going to be damaged by water.
Before you start the project and as you start accumulating the materials that you need to begin, you want to consider the following options to avoid water damage.
You can protect the concrete foundation of the home, and prevent potential flooring and drywall damage with waterproofing agents. A thick paint will be applied to all of the concrete, and it will act as a barrier. It stops water from passing through the walls to get into the basement, and from water that could flood inside the basement from an appliance. This is very affordable and a great preventative option to avoid condensation and moisture problems.
Tile flooring isn't going to absorb moisture like wood or carpeting can. You can get tile flooring to look like wood planks or natural stone, and it's easy to add a throw rug if you want to sit on the ground in some rooms. If you are worried about water and there is a problem, replacing a rug isn't nearly as problematic as needing to replace the whole floor. The tile is also easy to clean and isn't affected by changing temperatures.
Air Purification and Dehumidifying System
Having a unit that purifies the air to pull out dust and other pollutants, and that controls the humidity in the space will help keep the space dry. It will also help keep your furnace air filter less dirty. This can be a single unit that you run in the space, or you can have a system hooked into your furnace. This can keep moisture from moving from the basement through the ventilation system throughout the home.
Finishing the basement may be a risk because you live in an area where it floods, but you can try to pick water resistant materials and do other things to keep the space dry. Before you start doing any work on the basement, have a plumber check the sump pump to make sure it works properly, and to see if the unit will perform if you have a flood in the home. Find the professionals, such as Champion Waterproofing, and work out the details for the layout of your basement, and tell them you want everything as water-resistant as possible.