There's no Firefox extension for PiCore 13, so are you using a remote display again? Is the computer Running Firefox also running Tiny Core? The --kiosk option works for me with Firefox version 102.0esr running on TC 13 (installed with firefox_getLatest.sh), displaying over the network on another computer running Xorg (but it's not a Raspberry Pi).
The --kiosk option was apparantly added in Firefox version 71.
Perhaps try running Firefox with a clean profile in case some setting or extension prevents kiosk mode from working.