PokéBase - Pokémon Q&A
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I can't find the percentage, but as supplementary information, the effect of the White Flute wears off after 250 steps and has to be reused. - http://pokemon.wikia.com/wiki/White_Flute (EDIT: I know this is the White Flute article, but the Black Flute one doesn't give the steps)
Wait. The Black Flute decreases encounter rate, not the Black Flute.
Kronos, is that a typo?
You mean White Flute.
The white flute will double the encounter rate.

Source: Ultédex; an application for iOS.
Can you perhaps take a sceenshot?
Honestly, I don't know how...
If it's iOS, just press the lock button and the home button at the same time to take a screenshot. Then upload it to your computer and share it on imgur or another image sharing service.

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Best answer

It increases the encounter rate by 50%.
___
>Doubles the wild Pokémon encounter rate.


>When used in the field, doubles the rate of encounters with all wild Pokemon.


>Used outside of battle : Doubles the wild Pokémon encounter rate.

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