All that the signal USR2 does in the new flwm is cause flwm to rescan the content of the WM desktop menu. If you are trying to force a restart flwm, perhaps you can use kill with no signal specified (default quit signal) or a signal other than USR2.
It's a bit misleading that "kill" is just a signal-sender. It's up to each application to decide how to respond to each signal. There are some default responses and conventions so that "kill" is usually doing what the name implies, but it's not always the case.
EDIT: Would this work?
kill `pidof flwm` ; DISPLAY=:1.0 flwm &
--
Mike L.