How to attach/interface an ARM Cortex SoC with an stm32 processor
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 bootloading mode, and set up uart comms between your chips, you're good to go.

Cross platform Flash Tool for STM32