Intel processors with Braswell cores are very new (Dec 2015) and only available in a very small number ChromeOS devices. Braswell seems to be positioned as the replacement for Bay Trail, so this will likely change in 2016.
Factory firmware support for coreboot and SeaBIOS is uncertain but considered unlikely. Custom firmware is not presently available.
SeaBIOS support on Braswell may be possible, but there is no video BIOS, so SeaBIOS would not be able to initialize the GPU. GPU initialization on Braswell is handled by a UEFI GOP, and for that reason, Braswell support will likely be impossible until UEFI custom firmware becomes available and GalliumOS adds UEFI support. For more information about GalliumOS's plans for UEFI support, see Support/UEFI.
At the moment, your best option for running Linux on a Braswell ChromeOS device is probably Crouton.