I just upgraded to 2.8.1 via the Mac App Store and drag and drop from Skitch to Slack is broken.
Rolling back Skitch to 2.8 manually (https://evernote.s3.amazonaws.com/skitch/mac/release/Skitch-2.8.zip) allowed me to fix this issue.
I also tried the App Cleaner instructions above and reinstalling via the Mac App Store but it did not fix the issue.