T4 is not a OW terminal, but the general International terminal at JFK and is in fact operated by the same operator that operates AMS. The security lines are generic for all airlines as they have multiple carriers so in my recollection - it has been about six months since I went through T4 the priority lane is restricted to just passengers traveling in F and J and not other elites traveling in Y for the airlines flying there. At BA T7 and AA T8 you would have had access.
The priority security is enforced unevenly anyway. At the old T1 Flight Connections center at LHR there was a priority lane for BA F, J Gold and Silver fliers. OW elites in Y could not use it.