High-pressure sodium lights exhibit a "cycling" on-and-off behavior when
they reach end of life. However, when I've seen this it's been a
fairly slow cycle, and didn't exhibit the sort of bright strobe-like
flash you describe.
I suppose that you could be seeing a mercury-vapor lamp with a failing
bulb and/or ballast, where the ballast sends a strong pulse to
"strike" the lamp and get the arc flowing (hence the flash) and a
fault in the bulb causes an over-current or under-current condition
which then shuts down the arc almost immediately.
Pragmatically, you might want to write down the streetlamp pole number
(if it has one) and contact the city's public-works department and
report the problem.