I think the problem there is that by default, when you install the app again, it will have iCloud set as the sync. You would have to go into the settings (on iOS, right panel, button bottom-left), and change the sync there from iCloud to Dropbox. You need to change that setting on all devices.
If you want to clear the data in iCloud altogether, you could turn the sync to iCloud briefly on one device, and then immediately turn it off again. The app will ask if you want to remove the cloud data, and you could answer to remove it.
Kind regards,
Drew