I've run various releases of Tiny Core (11, 12, 15) from a USB pendrive without any problems.
One thing to note is that the eMMC Flash memory appears as mmcblk0 device. In the dmesg output:
mmcblk0: mmc0:0001 8GTF4R 7.28 GiB mmcblk0: p1 mmcblk0boot0: mmc0:0001 8GTF4R 4.00 MiB mmcblk0boot1: mmc0:0001 8GTF4R 4.00 MiB mmcblk0rpmb: mmc0:0001 8GTF4R 512 KiB, chardev (240:0)
I did wonder about the rpmb. Google tells me:
RPMB is a self-contained security protocol with its own command opcodes and data structures. The mechanism for this protocol involves a shared key and a HMAC (Hash Message Authentication Code), which is used to sign all the read/write operations accessing the secured area.This is something I haven't explored.