Normally, under the current schedule, there are 3 QF flights from Australia to LAX each day. A 747 from BNE (QF15/16), and A380s from SYD (QF11/12) and MEL (QF93/94). Some days there is a 4th flight, a 747 from MEL (QF95/96).
The LAX-JFK sectors of QF11/12 are operated by the 747 from BNE.
There tend to be delays to the return flights, often related to the JFK flight. There are a number of reasons for these delays, but they are most often caused by weather or ATC requirements in busy airspace on the transcon flight between two busy hubs. QF also sometimes holds the LAX departure to JFK when there are delays in customs and security.
The return flights from LAX to BNE, SYD and MEL are timed in order to make connections from JFK, however when there is a delay ex JFK, those connections can be impacted.
When there is a delay from JFK, the BNE flight will get delayed as QF16 uses the same aircraft as the QF12 from New York. If the resulting arrival in BNE is more then ~2.5 hours late, the next QF15 can also be delayed.
The QF94 is more likely to depart close to on time, even without the JFK connecting passengers as they only have ~2 hours with an on time arrival to turn the aircraft around in MEL for an on time departure back to LAX as QF93. They will only hold QF94 for connecting pax if the amount of people connecting is greater then can be handled by the other QF flights to Australia. On days where QF96 is operating, there is even less reason to hold QF94.
The A380 QF12 from LAX can depart before the 747 QF12 arrives from JFK. All that is required is changing the call sign so that there are not 2 "Qantas 12"s in the same ATC region at the same time. They will rarely do this however, due to the amount of people coming from New York and going through to Sydney usually being greater then the amount of seats available on the same aircraft once the BNE passengers starting at LAX are accounted for. If the load on QF16 is low enough to accommodate the connecting pax to SYD and MEL, there is no need to hold QF12 to SYD or QF94 to MEL.
If there is a long delay at JFK, and you are connecting in LAX to QF12 or QF94, depending on loading, you may miss those connections. However Qantas will ensure you get to where you are going, it may just require a domestic connection via BNE (QF16) or, on some days, MEL on the later QF96.
With upcoming changes to A380 flying and 787s arriving, from March next year, the delays caused by JFK may not be as bad as they have been.
I've only done the JFK flight once, in one direction. When there were 5 near daily Qantas flights to LAX (BNE, 2xSYD, MEL, AKL) and I was on QF107 all the way through (was actually on board when this photo was taken
Boeing 747-438/ER - Qantas | Aviation Photo #1382468 | Airliners.net ).
That flight was delayed departing LA for NY due to long lines for customs.