Not familiar with TinyCore myself, but I’d recommend trying Nerves Kiosk if a webpage kiosk is your primary goal [1]. Getting all of the FS settings right and a tuned system like daviduum talks about is tricky IMHO. Though it should be possible with Yocto Linux or similar as well I’d imagine, especially with ‘fwup’ or similar in the loop. Nerves uses ‘fwup’ [2] to create a R/O squashfs filesystem for the core OS image which is also highly compressed.

1: https://github.com/LeToteTeam/kiosk_system_rpi3/blob/master/... 2: https://github.com/fhunleth/fwup