The ornamental design for a flushometer handle socket, as shown and described.
FIG. 1 is a perspective view of my new design for a flushometer handle socket;
FIG. 2 is a front elevation view thereof. The top and bottom plan views would look the same as the front elevation view.
FIG. 3 is a left end elevation view; and,
FIG. 4 is a right end elevation view with internal components not shown.
The broken line showing of the flushometer handle and internal plunger in FIGS. 1 and 2 is for illustrative purposes only and forms no part of the claimed design.