Try this extension:

• pinchy: https://addons.mozilla.org/firefox/addon/pinchy/

Unless I'm missing something that works with the touchpad while holding the shift key. I was hoping to be able to just use the touchscreen and swipe forward and back like you can in google chrome.

You can modify the involved browser.gesture.* prefs directly on the about:config page.

On the about:config page it shows browser.gesture.swipe.left Browser:BackOrBackDuplicate browser.gesture.swipe.right Browser:ForwardOrForwardDuplicate

When I swipe left or right on the touchscreen it selects text instead of going forward or back though. Is there something else I need to change?

The pinchy extension should have added swipe.left.shift and swipe.right.shift prefs that you can use to get the command for previous and next tab and copy them to the swipe.left and swipe.right

prefs.set("browser.gesture.swipe.left.shift", "Browser:PrevTab");
prefs.set("browser.gesture.swipe.right.shift", "Browser:NextTab");

Preferences can be modified via Modify (String or Integer) or Toggle (Boolean) in the right-click context menu and by double-clicking the line with the pref.

• http://kb.mozillazine.org/about:config