Flowdock to Rally integration inherits the permissions of the first person to set it up for that flow.
Article ID: 188468
When trying to add "another" Flowdock to Rally integration to a flow, the user is not able to see the projects to which they have access.
Release : 1.0
Component : System Adapter - Component of CA-CIS VSE
This is because the Flowdock to Rally integration caches the credentials of the first user who setup the (first) integration for that flow.
If the second person has a higher permission level, they can take screenshots of the first integration, delete it and recreate it using their higher level permission set. Along with adding their own integration.