In all the regular (without "Super") you can only achieve a chain of 20, but once that is completed you'll be advanced to "Super" in which ever regular battle you've completed. Your chain can go as high as 200+. This is quite a feat if you're able to make it.
Hope I've Helped
At the time of writing, a Smogon Forums user named The Dutch Plumberjack has a streak of 3668. So keep trying; you'll get there one of these days. source Feel free to click on the source and comment on this answer if the record updates.
