The ttylinux root file system is an 8 MB ext2 file system; the file system image is compressed and resides in the CD-ROM image. After burning the CD-ROM image to a blank CD-ROM disc, or mounting the CD-ROM image via loop device, you can find the compressed root file system; it is boot/filesys.gz. This root file system can be used with a custom kernel that you make.
pc_i486, pc_i686, and pc_x86_64 ttylinux are built with Linux 126.96.36.199 header files. Linux kernels are not backwards compatible; software using the capabilities of a given kernel version cannot be expected to work with any previous kernel version. Using a kernel older than the kernel with which ttylinux was built cannot be supported in any way. With that described, with the small number of packages in the ttylinux system, ttylinux works to some extent with any Linux kernel from 2.6.0 upwards.
Your custom kernel needs to support all the hardware you want to use, plus some additional requirements for ttylinux itself.
A kernel used for running ttylinux needs to have ramdisk support, initial ramdisk support, and a default ramdisk size of at least 8192. Note the kernel configuration has a default ramdisk size of 4096, which is not big enough.
If you want to use the basic firewall script of ttylinux, your kernel also needs iptables support with the netlink interface.
A ttylinux kernel needs to support ext2 file systems.
If you want to add a telnet server to ttylinux, your kernel will need to have Unix98 pseudo terminal support and support for the devpts file system.