Q. I have to know that flute has taken dikhsha? how an when? Why gopis were angry on flute/ Why Radharani always talk to flute please be on side?

A.The answer to your question is found in Sri Vidagdha-Madhava (The Most Clever Krishna) by Srila Rupa Goswami. This is a drama written by him and in Act Five titled Radha-prasadana (Decorating Radha) there is a verse sung by Radhika. Text 17 says:

Radhika: (vamsim udghatya. sopalambham)

sad-vamshatas tava janih purushottamasya
panau sthitir muralike saralasi jatya
kasmat tvaya sakhi guror vishama grihita
gopangana-gana-vimohana-mantra-diksha 

Radhika: (revealing the flute, She says with scorn:)

‘My dear friend the flute, it appears that you have been born of a very good family, for your residence in the hands of Sri Krishna. By birth you are simple and are not at all crooked. Why then have you taken initiation into this dangerous mantra that enchants the assembled gopis?’

From this verse one can see that the answer to your question is:
1. Flute has taken diksha – how and when?
Flute has taken diksha (initiation) from Krsna with a dangerous mantra. Initiation means it is connected to Krsna when it is placed on His lotus lips. The dangerous mantra is the most enchanting and blissful music that the flute produces which attracts the heart of the gopis.
2. why gopis were angry on flute?
The gopis are only seemingly angry with the flute because when the flute plays, they have to give up everything and dance at the tune of Krsna.
3. why radharani always talk to flute please be on side?
Radharani is so much absorbed in the love for Krsna and is so much enchanted with the beautiful music from Krsna’s flute that She wants to always keep the flute by Her side. Jatila (Her mother-in-law always wants to take away the flute from Her because she wants to stop Her from meeting Krsna).