(1) flash memory will support only a limited number of read-write cycles, so intensive use of a flashdrive to do this will result in shortened flashdrive life, because memory used for temp files or swap may die faster
(2) how you proceed might depend on whether you want a flashdrive that will boot on many computers or just a particular computer
(3) some installations onto flashdrive won't be very secure: almost anyone could boot the drive and access files on it
You'll need first to get the appropriate iso: either the i386 or the amd64 depending on the kind of machines you want to boot
The simplest thing to try might be System >> Administration >> Startup Disk Creator on your existing ubuntu installation, selecting the appropriate iso and the usb flash and adjusting the persistent memory size to what you need
If that doesn't work, Wikipedia has an extensive list of tools:
http://en.wikipedia.org/wiki/List_of_tools_to_create_Live_USB_systemsI often use unetbootin, though I have used LinuxLive and the Ubuntu Live USB creator
Unetbootin is in the repositories, so you can install it easily on any ubuntu machine:
System >> Administration >> Synaptic Package Manager
I think it'll appear under Applications >> System Tools, but I'm not sure since I customized my gnome menus. I almost always use a previously-downloaded iso for this, since the auto-download options are limited
Not all flashdrives are equal, and not all installation methods are equal. I've sometimes used LinuxLive (on a Windows machine): some BIOSes are grumpy and just won't boot off a flashdrive that was created on a linux machine; I'm not patient enough to figure out why or what an appropriate workaround would be
There are other options, some of which I've tried and some not. The first time I ever did this I followed a long multipage instruction set that involved setting cylinders and doing a lot of other hokey-pokey dancing; it finally worked, but it was a nightmare
I once installed OSX to a flashdrive by plugging the flashdrive into a mac and running the installation disk to install on the flashdrive; I expect that drive wouldn't have booted on any other machine. One could probably do the same with ubuntu; I haven't tried it yet because I think it might goo up the grub menu -- it wouldn't have bothered me with grub but I'm not really comfortable yet with grub2