Okay, the formula for finding the probability of getting 2 shinies within a certain number of encounters is this: (1 - (inverse odds)^(total attempts - 1))^2. If you really want me to explain why it's this formula, I can explain it in a comment, otherwise just trust me on this one.
Odds within three resets (nine Pokemon seen):
(1 - (8191/8192)^8)^2 = 9.52859782e-5% or 1/1,049,472.
Odds within ten resets (thirty Pokemon seen):
(1 - (8191/8192)^29)^2 = 0.00124891265% or 1/80,070.
Bonus! Odds of Cyndaquil specifically within three resets (three Cyndaquil seen):
(1 - (8191/8192)^2)^2 = 5.9597369e-6% or 1/16,779,264.
Edit: Just double-checked my math and it looks like my formula was slightly off. Fixed.