the first thing I would do is try running Tomcat on Windows or Linux
and see how small you can squeeze the address space to get a ballpark
of feasibility. I don't think Tomcat was not designed with embedded
systems in mind.

I saw an articles some years ago about a webserver that ran on a
dime-sized computer.  So presumably there are webservers out there
designed for tiny machines.

Check out the links at http://mindprod.com/jgloss/jvm.html
for possible JVM candidates.

See Marco Schmidt's list of JVMs:
http://schmidt.devlib.org/java/embedded.html

There is a Blackdown Linux ARM port that requires Linux on iPAQ
http://www.blackdown.org/
It supports Java 1.3.1 which some version of Tomcat might run under.

Embedding and use of FLASH I would think would best be done with a
FLASH aware JVM that did not just use it like a hard disk, but that
could have class byte code preloaded into FLASH.

You might look into ARM Jazelle if there is any chance of using a
different processor. http://www.arm.com/products/esd/jazelle_home.html

There is also SavaJe.  See http://mindprod.com/jgloss/savaje.html

you might check out the links at
http://mindprod.com/jgloss/picojava.html for leads to see what various
chip makers are recommending.