You can use /lib/firmware or /usr/local/lib/firmware.
dkms is a debian thing - in tinycore you need to prepare the kernel source with the tinycore kernel config using the compiletc, ncurses-dev, perl5, bc and elfutils-dev extensions.
The extensions for the most recent version of tinycore are at repo.tinycorelinux.net/12.x/x86/tcz