There are two types of storage that you need to address. The first is when you are transporting it in-between trips. During these scenarios, all you need to do is keep the tube partially deflated and ensure it is not in contact with direct sunlight. However, if you are talking about storing it away for the winter season, then you should deflate the entire float boat and leave it in a well-ventilated area.
All the materials in a floating boat are waterproof and generally resistant to mildew, but it still does not change the fact that it is better to store them in well-ventilated areas.