When I flag an email on a Google Exchange account, 2Do does not pick it up

Please kindly read the Capturing Rules section of this article. Google accounts set up over Exchange are inherently buggy and should be avoided. Alternatives have been suggested in the aforementioned article. If you have set up Gmail over Exchange simply to take benefit of PUSH notifications, Google instead recommends you use their official Gmail app and setup the account using the ’Gmail’ option in Mail.app instead. Doing this will ensure the flag setting, for example, is carried from device to device.