Sometimes the foot joint of a flute, when connected to the body joint, can be hard to remove. A lot of the newer flutes are made tighter around where they connect. Therefore, making it harder to pull off. Usually, twisting it back and forth without applying too much pressure on the springs will work. However, after playing and warming it up, the metal expands even further making it even more challenging. Using simple science I have found a way to simplify the process.
When metal freezes, it expands. When metal is warmed, it expands. But, when metal is cooled but not frozen it contracts. Using this theory, place your connected body and foot joint into the fridge. It only takes about 3-5 minutes for it to contract. Then, take it out and twist the two joints back and forth, without applying too much pressure to the springs. They should come apart. If not, try putting it back into the fridge, and try twisting it again. If that doesn't work, call your local flute shop and have them take a look. They probably will not charge for such a simple job. They can also be very helpful if you have any other questions about the functions of your flute. Happy flute playing!