Flyweights are sharable instances of a class. It might at first seem that each class is a Singleton, but in fact there might be a small number of instances, such as one for every character or one for every icon type. The number of instances that are allocated must be decided as the class instances are needed, and this is usually accomplished with a FlyweightFactory class. This Factory class usually is a Singleton, since it needs to keep track of whether a particular instance has been generated yet. It then either returns a new instance or a reference to one it has already generated.
To decide if some part of your program is a candidate for using Flyweights, consider whether it is possible to remove some data from the class and make it extrinsic. If this makes it possible to greatly reduce the number of different class instances your program needs to maintain, this might be a case where Flyweights will help.