Let me guess, the bolt holes on the flexplate don't match the flange spacing on the converter. Am I right? The notes for that B&M converter state, "This torque converter requires a small 10.75 in. bolt pattern flexplate."
GM flexplates were produced in two diameters: 12.75" and 14". The 12.75" diameter flexplate had a 153-tooth ring gear. The 14" flexplate had a 168-tooth ring gear. GM also used three different bolt circles for converter mounting: 9.75", 10.75" and 11.5". Some 12.75" flexplates were drilled with either 9.75" or 10.75" converter patterns, while some were drilled with both. Similarly, some 14" flexplates were drilled with either 10.75" or 11.5" converter patterns, and some were drilled with both.
Edit:
On close inspection the flexplate you purchased is drilled with two bolt patterns - three of the mounting pads are drilled on a 10.75" circle - three of the mounting pads are drilled on a 11.5" circle. The smaller circle is the one to use; spinning the converter 60° in either direction should allow the holes to line up. The starter you selected can be used with both the 12.75" (153-tooth) and 14" (168-tooth) flexplates.