> A “flooding” ping sends a new ping packet each time a packet is received from the remote end

Uhm, no:

    -f
       Flood ping. For every ECHO_REQUEST sent a period “.” is
       printed, while for every ECHO_REPLY received a backspace is
       printed. This provides a rapid display of how many packets
       are being dropped. If interval is not given, it sets interval
       to zero and outputs packets as fast as they come back or one
       hundred times per second, whichever is more. Only the
       super-user may use this option with zero interval.