"Burn in" with headphones, where it does seem to be a factor at all, is minor - and appears to be more the effect of the pads softening a bit changing how the drivers are aligned and spaced with your ears. Ultimately, the results when audible at all, are subtle. I recommend just listening to music through them. No specific burn in process has been shown to have any significant effect with headphones.
With amps, especially solid state amps, burn in has never (as far as I know) been demonstrated to change their character in any way. No difference. Ditto cables. Nothing to burn in (mechanical change due to wear). Electrons don't care whether they've been down the same path for 100 hours or not.
Just listen to your music.
If you do not currently like the sound you get out of the system - "burn in" is unlikely to change the actual sound they produce in any way. You may, however, get used to it (psychological and acoustic acclimation - which are real, but not an actual change to the sound).
Edited by liamstrain - 10/12/12 at 12:34pm