Where can I get supplies to repair a wicker chair?

I'd try a hardware store, like Home depot or Lowe's

Don't know about Michael's; I might try Ace hardware, or they might know where. Of course, you can always search online and/or eBay.

Hobby lobby as well

Michaels offers wicker furniture repair kits, but you can also try Pat Catan's, and home Depot might have some things you can use