Dual AC Power Input on Audio Amplifier Board
Should I assume a phase shift of 180 degrees?


Yes. The LM1875 uses a split supply. You need a transformer with a center-tapped secondary in the range 12-0-12 V to 22-0-22 V. The primary should suit your local mains supply, of course.

Does the board manufacturer suggest a suitable current/VA rating for the transformer? If not there is an application note on power supply design here.