Make sure that you are reading data for the correct game. On PokemonDB's Gen 2 learnset page for Nidorina, it says Nidorina can learn Poison Sting at level 19 in Gold/Silver. Nidorina's main Pokedex page lists Gen 8 games where the level is different, so you shouldn't read that if you're playing Gen 2.
We'll need something more scientific than just your word that the flinch chance is incorrect. You can trial it many times (preferably hundreds) to approximate the flinch chance, but you'd probably be wasting your time as Gen 2 games have been thoroughly researched and other sources agree on the flinch chance of 30%.
Other sources also agree that Cyndaquil cannot learn Earthquake in any game. If you're playing a modded game then I'd advise checking many sources before concluding that existing knowledge is incorrect.