I just did some testing using the Worldbuilder. When a city is built on flood plains, it removes the flood plains descriptor. So, putting your mouse over the terrain, it will no longer list flood plains. It will instead just note that you have fresh water. Now, if you go and add flood plains AFTER the city is built, you will get the full effects from flood plains and it lists flood plains as a descriptor. So, it is programmed to remove the effects of the flood plains except for the fresh water effects when city is built.
Hills/Plains, on the other hand, doesn't change when a city is built. Thus, why it gives the additional +1 production. Not sure if this was intentional or not. But, it has been discussed quite often in threads about best starting locations for cities. The Developers obviously know it is working this way. It had to be working this way throughout much of beta. I seems likely to me that it is there by design. But, I admit that is still just my opinion. I do agree that flood plains should add some food to a city that builds on it. But, I am fairly sure they didn't want to give you the full effects which is actually +3 food. Might be why you get no added benefit instead.