Further discussion
An unregistered editor just edited Oregon State University and asserted that it's a flagship university citing only this reference.  It's a reliable source but it's really, really weak evidence for such an important claim.  The paper was released ten years ago and classifies institutions as "flagships" based on data that were already over ten years old when the paper was released which means the data are now more than twenty years old.  The document was published as an NBER working paper which means that it may have undergone some sort of review process but it was not published in a peer-reviewed journal or other venue where we are assured of editorial oversight and quality control (although I assume that the NBER has those kinds of mechanisms in place; I just don't know for sure).  This single piece of weak evidence is entirely insufficient to justify such a strong claim.    
Here's an article that references OSU as a flagship university that also passes WP:RS and is far more recent: Source.   
That doesn't explicitly call OSU a flagship though, just that according to the author of the article there are two flagships. For all we know the author could think WOU and EOU are the flagships. Personally, I think OSU shouldn't be listed as flagship  if you do a quick search for UO's flagship status, there are comparatively many many more sources backing that up. 65.78.144.35  
Actually, the The Bulletin article implies that the chancellor of the Oregon University System said that the two institutions are flagships.  But it's not a direct quote so it's not entirely clear if that is something the chancellor said or the reporter's opinion or interpretation.  Without knowing which of those two possibilities is correct, this is pretty weak source, too.
There have been several discussions and edit wars about the flagship status (or lack thereof) of several universities lately so I apologize if I'm repeating myself but I urge you to consult the sources in Flagship; they're pretty good sources and include many of the most authoritative on this very subjective, murky, and ill-defined topic.  You'll be on much better ground if you can cite sources written by experts in higher education.