Hope this helps other Linux users on their Chromebooks with the BayTrail hardware.
I bought a new FHD Toshiba Chromebook, installed Mint 17.3 Xfce4 on it straight away (modified the BIOS & conductive sticker).
Everything rocked except for the sound.... my symptom was that I only had the HDMI outputs, no speakers, no analog.
To fix this I did the following:
Update the kernel version from 3. something to 4.2.0-23 by using the update manager. (start the gui version of the update manager, click View > Linux Kernels, click at least the 4.2.0-23 version)
Update / install the linux-firmware package:
sudo apt-get install linux-firmware
Download this Intel blob (click the link to download)
https://kernel.googlesource.com/pub/scm/linux/kernel/git/firmware/linux-firmware/+/refs/heads/master/intel/fw_sst_0f28.bin-48kHz_i2s_master
Store it here:
/lib/firmware/intel
Download the modified sound config file (asound.state) from https://gist.github.com/n1trux/3751a87f374a8af5f611
Open a terminal window and type
sudo alsa force-unload
This temporarily kills the audio services.
Replace the system’s sound config file with the downloaded version:
sudo cp ~/Downloads/asound.state /var/lib/alsa
Reboot, open pavucontrol and unmute your analog speakers, also perhaps check alsamixer: speaker should be enabled or allowed to be enabled.