Flood plane is geographically correct. This means, an area that does not have an undulating surface that is fairly level, or without elevation. Plane is attributed to flat surface where water percolates, while plain could be used for being straight forward in terms of attitude or openness in mind.

Another Answer:

For normal use, it is: FLOOD PLAIN. Here is an example sentence: Even if a home is not in a flood plain, it is a good idea for a homeowner to purchase inexpensive flood insurance.

It's called a 'flood plain'.

The tsunami can flood as fast as a commercial jet plane.

Because London is built on the ancient flood plane of the river Thames.

An alluvial flood plain and /or a delta flood plane.

That could also describe a vernal pond, bog, marsh or some other type of wetland.