Recently i did a session on integration monday covering how you could do automated testing of Logic Apps with Specflow.
The video and slides are available on = http://www.integrationusergroup.com/automated-testing-logic-apps-specflow/
A few people have asked for the sample code i used, this can be downloaded below
Please note that i have modified the logic app in the designer to remove subscription guid and also other settings from the tests config file. You will need to supply your own settings for these.