Theory on MedalBonuses

As Gamepress has scientifically prooven, after the final catch rate (FCR) is calculated (Including species base rate, razz bonus, throw modifiers and such...), this rate is compared to a random percentage (RNG%). If this RNG% is lower than FCR, the Poke stays in.

As for MedalBonuses, theories tend to point to multipliers and percentage modifiers. but I think it is not a multiplier or a percentage. I think they simply redraw the RNG%, for the number of MedalBonuses you have, until the Poke stays in, or you run out of MedalBonuses.

Let's say : When you have Medal Bonus+1, if the poke isn't caught at first draw, they will randomize again, and if this 2nd RNG% lower than FCR, the Poke stays in.
If you have MedalBonus+2, they might randomize again (If Poke didn't stay in 1st or 2nd try), and yet again for MedalBonus+3 (If Poke didn't stay at 1st, 2nd or 3rd try).

So, having BonusMedal+3 wwould be the same as throwing as much as four balls at the poke (With the added plus of not having the risk of him fleeing in between balls).

So, when Medal flashes after successful catch, means it was caught with one of the additional random draws.

This is how I think it happens, although I absolutely have no scientific data to back it up, just seems logical.