Klingons would never wear federation uniform,

the Quote that springs to mind, 'A Child's uniform'

Besides, its a bit farfetched that starfleet's current dress code would allow uniform from a faction that they are currently at war with, (excluding the odd spot of espionage)

But who knows, i remeber being told feds cant get I.S.S. prefix because we are still the federation in terran ships, and look what happened :/