A state must have only one flagship for the same reason that a naval fleet must:  the word "flagship" itself is an attributive superlative.  The two definitions of the word are "1. In a maritime fleet, the ship occupied by the fleet's commander (usually an admiral); it denotes this by flying his flag.  2. The most important one out of a related group."  The second definition obviously suits this dry-land discussion.  Each state cannot have two universities which are both "the most XXX."   

 The sole non-local source cited in support of Kansas State's claim for flagship status, the USA Today article, has been shown to be unreliable and/or suspect even within the USA Today's archives.  The multitude of official sources (including, as was mentioned above, the College Board to which Kansas State University is a member) concurrently list a total of 50 and only 50 flagship universities (each time offering only one per state, and each of those schools remaining consistent).  The consensus of authoritative sources is clearly that there is only one flagship university per state.