I found the chart you referred to online. Indeed this is a JetBlue “owned” procedure. Jeppesen does publish the chart, but it is only made available to JetBlue clients, and is not part of the public Jeppesen chart database.
In the case of a “private” procedure like this, the airline will directly contract with the FAA to certify the procedure, and to reimburse the government for the costs associated with doing so.
The r/w controllers at JFK are of course aware of the procedure, but cannot and will not clear any aircraft other than JBU to fly it.
A typical RNP AR approach will contain the phrase “AUTHORIZATION REQUIRED” in the chart notes, which indicates the aircraft must be properly equipped to fly it, and the flight crew must have specific training.
The RNP 13L approach at JFK has an additional chart note: “USE OF THIS PROCEDURE REQUIRES SPECIFIC AUTHORIZATION BY FAA FLIGHT STANDARDS”. That is the indication that it is a private procedure that is only available to certain operators.