The blinkers are run by the BCM which sounds like is having a problem. Usually the blinkers will turn off with the key if it was something like a switch but the BCM stays live with the key off.
To find out for sure we must scan the CAN here is video to show you how.
If it is the BCM you will need to have a shop program it for you it should cost about $130.00
Check out the diagrams (Below). Please let us know what you find. We are interested to see what it is.
Images (Click to enlarge)
Thursday, September 21st, 2017 AT 4:22 PM