Installation: The ideal way to install a small Linux setup on a PC110 is to have a PCMCIA disk deivce handy (ethernet won't help you as you can't get the ethernet driver onto the PC110). If you have a PCMCIA disk around you can boot the PC110 off that disk, copy a couple of magic files onto the flash, maybe throwing out some of the existing stuff and off you go.
For the truely masochistic it is possible to install Linux on a PC110 without having the loan of a PCMCIA drive and something to write onto it. I'd strongly suggest you find a drive however as it is painful. Firstly you need to make some space on the flash drive for dumping files. Having done this make sure the modem is on auto-answer. Plug it into a phone and type COPY COM1: MY.COM. On another machine .BOO encode a terminal program like kermit and put the ascii deboo on the front of it (its on micros.hensa.ac.uk) - its a PC binary written in assembler that compiles only to ascii symbols. After you've copied all the data drop the line from the uploading end and run MY.COM on the PC110. If it worked you have a sane comms program and can now use it to upload the mini UNZIP and the ZIP files of the minimal Linux at 2400 baud.
Tiny Distributions: There are several "small" Linux distributions but only one IMHO that is small enough and fits the job. It's actually meant to run off a floppy but works remarkably well if you put the kernel and compressed ramdisk image onto the flash drive /dev/hda1 and also tell the machine to mount the /dev/hda1 disk as home so you can use the rest. The down side is that you get an MSDOS file system for /home so use UMSDOS on it.
You can get the miniature HAL91 distribution from its home site.
You'll probably want to customise it as its fairly heavily.