You may. CX publishes a mileage based fare PHX-SIN with a maximum permitted mileage of 10912. As AA will let you exceed this by 25%, you can route through JFK (or LAX or ORD or SFO or YYZ or YVR). Of course to get to JFK from PHX you must connect in ORD, DFW, MIA or LAX. If traveling in F I might route PHX-LAX-JFK to enjoy AFS and spend a few days in New York before heading to HKG.