When taking apart your flute, you will disconnect the head or the mouthpiece of your instrument first. This part of the flute is medium in length and so you are looking for the medium space in your case, and it is the part you will want to locate first. The space provided for the head of the flute will be easily identified by a slight bulge at the top of one end of the space. That is where you place the end closest to the mouthpiece, face up.
Identifying the longest space in your case is the easiest. The middle part of your flute, the longest part, will go into this space again face up with all the keys outwards. The smooth part of your instrument is the part that goes face down in the lined space in your case. Usually the longest space takes up the length of the case, with the two other instrument parts next to each other in front of the long section.
The foot of the flute is the instrument's smallest part and so fits into the smallest space in the case. Usually it is the last part of the instrument you will pick up to assemble or put away when disassembling your flute, so there will be nowhere else for you to put the smallest piece. Again the smooth side of the foot goes face down into the space provided, with the keys on top.
Cleaning tools can be made of plastic or metal, but regardless of the material, their shape is the same: a very long thin stick with an eye-of-a-needle style head for pulling through a cleaning cloth. Because of its shape, it may be that your cleaning tool space is not immediately obvious. Usually a shallow dent along the side of the case, it is normally located either in front of or behind the spaces for the flute. If furry fabric prevents you from seeing it, feel along the sides for a long indentation.