Memo to Rizzo, for 2013, find a catcher who can call a good game, throw out base stealers and hit .300.
I went to Fangraphs and found all the catchers who, in 4000+ plate appearances, maintained a batting average over .300. They are: Joe Mauer, Mickey Cochrane, Bill Dickey, Deacon White, Spud Davis, Mike Piazza, King Kelly, Ernie Lombardi, Victor Martinez, and Buck Ewing.
Of these, two are active: Joe Mauer and Victor Martinez. In 2012, Joe Mauer has caught 11.9% of baserunners (5/42), an almost identical line to Jesus Flores (5/45). In his last full season, 2010, Victor Martinez caught 21.6% of baserunners. This is well below average.
The player you want does not exist. QED.