You're getting these all at random. This is a Twitch problem, and they're real people, not bots. These people hack them in by the boxfuls and wondertrade them all away.
All you can do is pay attention to when the streamer is doing a giveaway for the respective Pokemon and hope you get lucky enough to connect with one.
I would also be inclined to believe you'd have a harder time finding someone who will be participating in such events in older games.