Twitter is closed. Unless Devonthink offers an official way to communicate with Twitter there is no way to import the data into other systems. They now also have removed their RSS feeds. You might want to try alternatives like app.net, which are more open.
I was and am still ‘following’ some tweets by reading them as RSS with DEVONthink Pro Office. After Twitter has removed the old API, I’m currently using http://www.rssitfor.me/
Searching the web, it seems there are also solutions available for folks geekier than me and who knows how long the one linked above will stay, but as said, currently it works.