This fare opens up in late September but is valid for travel through the end of the booking schedule in March 2019. Flights are available daily, but you'll want to fly via LGW in order for the connection. Flights through London (LHR) will require a change of airports and should be avoided for this particular fare.
From Jersey, you can take a ferry over to neighboring Guernsey in the Channel Islands or a short hop over to France where you can explore the coastline of Normandy. With this great fare, you can get creative with other side trips that would normally cost quite a lot more.
Searching on BA.com, I found seats departing JFK on Monday, September 25, and returning from JER on Monday, October 1, 2018. As I mentioned before, dates are widely available for travel in the autumn and winter months.