How can I identify the aircraft’s phase of flight in this picture?
It is much lower than cruise altitude, I would guess roughly 4000-6000 feet.  The flaps are up because it is neither taking off nor landing.  Generally flaps are deployed around 2000 feet or below.  Given the proximity to New York City it is probably flying an arrival or departure procedure.  

If you really wanted to dig deeper you could determine relative position and from Manhattan in the background and compare against published procedures into and out of the city's airports.