STM32's have a serial bootloader built in. See http://www.scienceprog.com/flashing-programs-to-stm32-embedded-bootloader/
STMicro makes a Flash tool to get at the bootloader. If you can find a version that runs under Linux, do some switching to put the STM32 into booloadingbootloading mode, and set up uart comms between your chips, you're good to go.