Brian Campf, who sent this photo along, identified Williams by comparing the photo with this shot of the 1928 St. Louis Stars—Williams is in the back row, second from right (it’s the same shot used for Williams in the Seamheads DB, by the way).
But what’s interesting here is not so much Flick himself, though it’s a fine photo of him. It’s what’s in the background. Williams is wearing the uniform of the St. Louis Stars. From 1922 through 1931 the Stars played in Stars Park, where left field was cut off by a city trolley car barn. It was only 250 feet down the left field foul line.
As Brian points out, if Williams is pictured in Stars Park, then we’re looking at the left field line, with third base to the right of Williams (where a player is standing with hands on knees), and home plate would be either behind or slightly to the left of Williams. And down the left field line, after the grand stand and taking the place of a left field wall, is certainly what looks like a building to me, rather than an outfield wall in a ballpark. Could this be the famous trolley car barn?
If so, this would be the only real image of Stars Park I know of (aside from backgrounds to team photos such as the one of the ’28 Stars above).
UPDATE 7/24/2014 Scott Simkus pointed out that these photographs, of St. Louis Stars Willie Wells and Cool Papa Bell, also show the same structure in the background, which he has always assumed was the trolley barn.