FYI saythatagain the ESTA does ask for the outward flight number (you would need to insert the name of the airline from their drop down menu). This has always been a requirement of the US govt. Not all the details on the ESTA are mandatory but that one is.
All details need to be right, you cannot afford to make any mistakes with such an application at immigration.
Only use the official US govt website which is https://esta.cbp.dhs.gov as there are many websites out there who charge a lot of money and many of these are scammers (that site you originally looked at is not a good one to use).
I would reimput her reference number (that very long sixteen digit and letter type one) and reimput the correct flight number. I think this can be corrected that way.