Mostly, the app description talks about sound through the cell phone speakers. It only briefly mentions testing headphones, presumably with the headphone jack, it the phone has one.
The speaker related stuff is not helpful. Further, if I were going to make a jumper cord from the headphone outlet, I would want to put a large capacitor (like 100 ufd) in series with the signal to prevent any kind of DC coupling between the device being tested and the cell phone.
I don't think I would do this. It's too easy to do something similar with a PC sound card and it is generally safer for the equipment. There are some inexpensive signal generators around as well. The question comes up about THD - how clean is the source? Sound cards do pretty well, low cost signal generators may be pretty awful. Real Arbitrary Waveform Generators can be very good. It depends on what you expect.
If it was for injecting a signal into a device that isn't working, I would buy one of the cheap signal generators and save on my cell phone or PC.