The noise from a flash charging is from the inductor/transformer, not the capacitor.
Capacitors can make sound, but much more rarely and softly. The core materials used in inductors and transformers are magnetostrictive (i.e., their dimensions vary with the applied magnetic field). Also, the windings can change shape as the magnetic field varies. Many transformers are dipped in goo to dampen the audible noise (and to reduce sensitivity to moisture, etc.).
Capacitors have plates that are separated by such small distances that, even if the plate separation were to modulate as a function of applied electric field, the sound emitted would be feeble.
Failing electrolytic capacitors can generate electrical noise -- a steady voltage can produce currents that vary randomly, crackle, pop, whistle, chirp, etc. If these capacitors are in the audio signal path, then the electrical noise can turn into audible noise.