In order to update the fc firmware, you need to put it into whats called dfu or bootloader mode. This allows you to access the processor directly and load new software/firmware to it. Some flight controller's will automatically enter this mode when you press the flash button in betaflight but most others require you to set this manually. We use 1 of 2 programs to do this through the computer called zadig or impulse rc driver fixer. Impulse rc driver fixer is the easiest one as you just plug in the fc and run the program, it will automatically set the driver to dfu so its ready to flash in betaflight.
For esc firmware updates, you will connect to blheli or blehi32 (depending on which esc model you are using) through the fc (flight controller), so you plug in the usb, power up the drone and open the esc configurator (blheli/blheli32). If it doesn't recognise the esc's then you ned to check that the proper com port (usb port) is selected for the usb and that the fc passthrough setting is selected (blheli setting needs to be set to fc passthrough to recognise esc's from the fc).
Some computers won't have the needed drivers installed to recognise our flight controllers and esc's so make sure your computer has the latest stm32 driver packages up to date. If you still have problems contact us for further assistance.