While the MAX98307 can provide the power to the load needed for the application (see Figure 1 taken from the MAX98307 data sheet), one design suggestion to keep in mind is the noise introduced by the MAX98307 may be too high for headphone applications.
For example, take a look at the MAX97220A which has an output noise voltage of 7uV and compare it with the MAX98307 with an output noise voltage of 52uV. If the intended application is 300Ω headphones, the MAX98307 output noise will most likely be heard given the proximity to the ear. The MAX97220A on the other hand will have a much lower noise and be more suitable for headphone applications. Also note that the MAX98307 is a Class D amplifier with a differential output which means it would have to be located close to the speaker. If you need the MAX98307 for a headphone solution, then you need to locate the IC as close as possible to the speaker since the inputs are ground referenced. In other words, placed directly into the headphone transducer, not at the jack end of the headphones.