A zipper opens and closes in one movement, so it is read as how easily you open up or shut off. A stuck zipper is linked to frustration at something you cannot release or seal.
When this appeared in your dream, what were you feeling?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.