It signifies Lord's askalitha brahmacharitva (means perfect/eternal celibate).
Lord wears it to signify that his a ajanma brahmachari/nitya brahmachari. It is proven when Lord revives the foetus of the womb of uttara.(who is none other than maharaja parikshit son of abhimanyu).
Peacock is the only species which doesn't reproduce through the samyoga of male and female reproductory organs, the peahen collects tears of peacock(which contain reproduction cells) and lay eggs.
If we dwell deep in to it, we can understand the eternal relationship of Lord with Gopis and his 16108 wives.
The flute is symbolic of the spine which has apertures. On activation of all the chakras, the vayu blows through this spine in the sukshma sharira and enables the tapasvi to do sattvic karmas and other high class siddhis. Swami Sivananda had written that on reaching closer to the inner divine a tapasvi hears the sound of the flute and bell inside his head. (not like a hallucination).
Peacock feathers have crystals which enhance the powers of the pineal gland which too have similar crystals. The colours of the peacock feather are the same as that of the sun seen in NASA photos, and the surya bija mantra '”Om Hraam Hreem Hraum Sah Suryay Namah” activates shaktis as described in Ram and Krushna Leelas. Peacock is also vahan of Kartikeya who is metaphorical 'son' of Siva, or the divine powers produced by meditation on Siva.
...Why does Krishna have the peacock feather on his head? A king is
responsible for the whole society and that responsibility can become a
burden, which sits on the head as the crown. But Krishna fulfills all
his responsibility effortlessly, like a game. A mother never feels
taking care of her children is a burden. Similarly, Krishna wears his
responsibility lightly and plays his roles colorfully, just like the
peacock feather on his crown.
...In the presence of pure bliss, joy, all complaints vanish and life
appears like a play. One can look at every trouble as a challenge or
can spend it crying and complaining. You know, what you have in your
hand indicates what you are inside. If you have a gun in your hand, it
indicates fear or violence. If you have a flower in your hand, it
indicates you are like a flower. If you have a flute in your hand, you
are like a flute — hollow and empty.
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