Flat handlebar caliper brake compatibility
The product you are looking for is interrupter levers. regular flat bar brake levers aren't designed to work in conjunction with STI levers.  The ones I linked to specifically say they are compatible with caliper/cantilever brakes.  I'm pretty sure most interrupter levers would be compatible with caliper/cantilever brakes because v-brakes don't tend to be found on bike with drop bars, which is where one would normally need interrupter levers.