To check bags all the way through, will require interline agreements B6=BA, B6=VY and BA=VY to cover the software side of placing a bag into the load of a particular flight, and also covering the physical handover of the bag at JFK and ORY.
Whilst having an interline agreement is necessary to permit baggage transfer, it doesn't mean that it will occur, as the flights are on separate tickets. As mentioned above it's in the control of the B6 agent at AUS.
B6 don't appear to have any published policy on checking through non same ticket bags, so best to plan that they will not, but YMMV.
JetBlue will usually arrive into JFK T5. If Jet Blue won't check through to ORY or BCN you will need to collect bags, and allow time to transfer to T7 with your bags.
At T7, check in with Openskies to ORY, paying any applicable baggage charges (if any).
BA/Openskies will not check through to a Vueling flight as Vueling is not OneWorld, so if JetBlue will not check all the way through AUS to BCN, you will need to collect in ORY.
Openskies is generally terminal West at ORY. Vueling is generally also West. You will need to enter France and collect luggage, then check in with your bags, so allow time.
Check in with Vueling to BCN paying any applicable bag charges (if any).
There's a thread here with some more info on non through ticket bag transfers:
http://www.flyertalk.com/forum/briti...e-tickets.html
Good luck with a relatively complex itinerary.