The chance of getting a shiny Eevee in Gen 4 is 1/8192, while the chance of getting a female Eevee is supposed to be 1/8, but due to a programming quirk, is rounded to 12.11% (as opposed to 12.5%). Multiplying these, we find that the chance of a female shiny Eevee (in any single encounter) is 0.001478271484375%.

To find the cumulative chance after 2536 encounters, we run it through the cumulative equation, B(n,p), and get

1 - (1 - 0.00001478271484375) ^ 2536 = **3.68%**