Hmm, I'm not sure I understand the part about the flesh paper doesn't stick. You mean it doesn't stick to the mat?
Each piece of the picture has to be cut separately and then assembled. So, for example, if you were doing Ariel on page 29 of the Dreams Come True book, you'd cut Ariel out by pressing the Ariel button on its own on whatever color paper you want to use for the base. Then you'd do the flesh part by putting flesh colored paper on your mat and pressing the layers:flesh/hair key and then the Ariel button, the flesh would be cut. Then put the red paper on for her hair, be sure the layers:flesh/hair key is still lit up, then press shift then the Ariel button to cut the hair. Then use purple paper and press layers

utfit/outfit then press Ariel to cut her shirt (for lack of a better word). Then put aqua paper on your mat, keep layers: outfit/outfit lit up then press shift then the ariel button to cut out the bow for her hair.
When you look at the different sections of the booklet, each little square has two pictures. The lower left picture is cut by having that feature lit up and hitting the button. The upper right picture is cut by having that feature lit up AND pressing shift before you press the key.
HTH