Hi there,
Not sure if this will work because it is from chrome on an s4 mini but I looked and looked for days and FINALLY FOUND IT!! On the top of the screen, usually right side, there are two squares with a number in it, that is the number of open tabs. Click on that and it should bring you to the tabs screen. Once in that screen hit the menu button, or the action button, on phones its on the bottom left side, its the equivilent of the right click on a PC. Anyway, once inside the tabs screen, that button will offer "close all tabs." BUT ONLY ONCE YOUR IN THE TAB SCREEN, if you are actually in a tab using the browser, it won't be there.
Hope that helps!!
Ben