>Pokémon encountered in the Friend Safari have a 1/512 chance of being Shiny, or eight times more likely than normal; this chance is unaffected by the Shiny Charm.
-Bulbapedia
According to Bulbapedia, the chance is 1/512 and is not affected by the Shiny Charm.
However,
The source for that information comes from tests made by people on Smogon. Because of that, we do not know for certain about Friend Safari shiny rates. Tests seem to suggest that the Shiny Charm does not affect the shiny rate (which is guessed to be 1/512), but no one knows for sure.
You can see their test results here.
