For information, Amex Travel (USA) is not operated by American Express. It is outsourced to Orbitz which is owned by Expedia. At one level this does not matter because American Express is responsible for choosing Orbitz, but it may prove helpful when trying to understand claims such as "...did not send the funds for the ticket to jetblue...", because that may be something the travel agency failed to do rather than the credit card company.

On your statement (or online) does the airline ticket purchase appear as a JetBlue transaction, or were you charged by the travel agency?

Disputing a duplicate charge from a hotel is routine.