The datasheet shows that chip PWM input frequency must be in the range 100 to 1000Hz, which may
be the flicker issue - go for the higher end of this range. The noise from the inductor
will be down mainly to the PWM frequency I think (the switching frequency is ultrasonic). The inductor may
be mechanically resonating. Its a fact of life with high current switch mode supplies that the inductor
will vibrate due to magnetostriction. Whether that vibration is a problem depends on the frequency,
the mass of the inductor, whether the PCB has a mechanical resonance at that frequency and probably
many other factors.
If the inductor is also getting hot I'd suggest go for a larger inductor (same inductance, higher current rating)
as that might solve both issues.