Once you reach a total of 500 battles for a Pokémon, the odds (with the shiny charm) are 1/512, just like the Masuda Method.
However, (and this is a big one lol), the method only works 3% of the time. This was likely a glitch that Game Freak is not fixing, but it is not confirmed.
So, overall, Rookidee has a shiny chance of 1/512 3% of the time, and a 97% percent chance of having the regular shiny charm odds, being 1/1365
I Hope I Helped! (Good Luck on the hunt)
Source: Prior Knowledge & This