Hi Josh,
Yes, you can reflash the BLE112 module, but you'll need the TI CC Debugger to do it. The back of the BLE TinyShield has 6 pins on it which are the programming connection, you'll need to wire these over to the CC Debugger connector (the schematic for the BLE TinyShield is on the website to see what the pins are) - this is how we load in the initial program into the modules.
Thanks,
Ken
TinyCircuits