@njathan
I don't own a Pi3, as I'm considering it a flawed product - CPU overheating & throttling & unable to hardware disable Wifi&BT wich both are flawed due to the Broadpwn exploit (they got an official patch some days ago), so I'm not sure I could help you with the BCM chip id.
Compiling a kernel module is always tricky, it's like in electronics, everyone has a schematic that doesn't work - in this respect, everyone has a howto that will break the compilation/module/kernel. Additionally, in order to compile only one module/driver you'll need at least the Raspberry kernel headers and the kernel .config file. Having this said and assuming you are using the latest Raspberry official kernel on your Slack ARM, I'd strongly suggest you to get a Raspbian image (the complete/big one), boot it on your Pi and follow the instructions from nexmon - as they are working& tested. After you finish the compilation&modules installation, archive the results by running:
cd /
tar -czvpf kernel-WiFi-patched-kernel-version.tgz /lib/modules /lib/firmware
- backup the resulted archive on an external stick/HDD
- boot with your Slack-ARM SDCard
- backup your Slack-ARM by running:
cd /
tar -czvpf kernel-Slack-ARM-Backup-kernel-version.tgz /lib/modules /lib/firmware
- copy your kernel-WiFi-patched-kernel-version.tgz in /
- run:
cd /
rm -rf /lib/modules
rm -rf /lib/firmware
tar -xzvpf kernel-WiFi-patched-kernel-version.tgz
/sbin/depmod -a kernel-version
- reboot your Pi and you should be good
- in all the above instructions you should make sure that you have the same kernel-version on both Raspbian & Slack ARM
and check it with uname -a. In the instructions substitute kernel-version with the output from uname -a - for example 4.9.28-v7+
If you're not familiar with dd and backing up your SDCard under Linux, then you can go for the Windows solution - works well!
https://sourceforge.net/projects/win32diskimager/
Have fun!