If you know Jack
A few weeks or months before the call, you could create a simple web page with a login wall and a signup page. In order to sign up, you need to write your phone number. By using standard measures, you can hide your access to the website, hide as much as possible the website in the deep web and protect the database.
You now need to tell Jack the URL: this can be done in different ways, including using a standard dead drop or - if you are Jason Bourne, it should be a piece of cake- by breaking into Jack's house and putting pieces of paper with the URL in the pockets of every trouser,jacket,etc. he uses (obviously the pieces of paper must not be handwritten, and you must check the absence of watermarks on the paper, so to avoid identification of the printer).
At this point, you and Jack separately buy your burner phones. Jack uses an open wifi network to access the website and write his phone number in the database. At a given time, you log in, retrieve the number from the website and write it. The website can be built in such a way to delete its content after been accessed twice. You are now ready to call Jack.
The tricky part is guaranteeing that the other phone number written in the database is actually Jack's and not Mike's (Adm. Michael S. Rogers). This can be achieved by agreeing codewords to be used at the beginning of the phone call (which can be written on the above-mentioned pieces of paper).
Jeff Meden suggested the possibility of a man in the middle attack. Basically, the scheme outlined doesn't prevent Mike from replacing the number entered by Jake with his own number and setting up a relay to forward calls to Jake's burner phone. In this way, Mike could be able to listen the conversation between Jason and Jack.
This attack could be thwarted (thanks again to Jeff!) by encrypting the data entered in the database (in this case, Jack's number) with a pad written on the pieces of paper planted on Jack.
Of course, if a history mechanism doesn't exist, Mike could arbitrarily alter the ciphertext, knowing that if the corresponding plaintext is not a valid phone number, the call will not take place.