First, which Linux distribution/version are you using? We developed the Eggbot under Ubuntu, and we’ve had scattered reports of success with other distributions as well. (And, one person reported having trouble with Gentoo last year, but we’ve been unable to reproduce the setup locally.)
Second, check to see if the Eggbot has shown up as a USB-ACM interface on your computer. The EiBotBoard (EBB) normally shows up on linux machines as /dev/ttyACM* (e.g., /dev/ttyACM0), so look for it there.
If it is present, try again from Inkscape, at least twice in a row, to see if you can get a connection.
You may also want to consider unplugging it and plugging it back in, trying a different USB cable (if you have one handy), or if you are using an extra long/thin USB cable or hub, going back to the original cable for testing.
We have seen some suggestion that USB devices may not register on linux until after a restart, but I’d try that only as a last resort.
Please let us know how it goes!