K.W.
My 5 year old has been like this since we took the paci away at 2 years old. She is constantly chewing her nails, or anything that will fit into her mouth. She chews up her sleeves, toys. Sometimes I think she's part puppy. I have no advice, sorry.
I did notice however that the more attention I bring to it, the worse it gets. And she does it often when she is bored. Keeping her hands busy seems to help a little.
On a similar note...I caught my 3 year old cleaning the toilet seat with her toothbrush once. Yuck! Apparently, this was a regular habit for her. I'm glad I caught her!