Rick Sanchez? In character, I could see him hating Pokemon, thinking it saccharine with unbelievable science & too much anime. Annoyance who hopefully is dealt with quickly in all 3 rounds. At best, I'd bet he'd be exploitative.
Rick Taylor? Becomes a problem over time due to how the mask influences him. Driven by a quest. Let him stay a little while to sightsee if he wants but after that, Palkia or Jirachi or Arceus needs to get him out or something needs to fix him & his mask & rescue mission problem.
Rick the Fox's behaviour & intelligence are unclear, but because he's not a human & has a weather-manipulating crossbow, he might be mistaken for a new species of Pokemon, but I'd assume he has humanlike intelligence.
Rick Grimes, I don't know him, but I'd bet he'd probably be happy to free of the zombie apocalypse world, if concerned for the people he lead. Sadly, it is said "Can be mentally insane at times", so his reprieve from the zombie apocalypse could end shorter than expected. He maxes out at Wall Level with weapons, though, so he probably gets detained by humans, Pokemon not needed.
Rick, who is Kirby's friend? (Why doesn't he have named Keys for his two tiers?) Also probably mistaken for a Pokemon. However, being Multi-Solar System Class, he's easily the most dangerous. Thankfully, tier doesn't equal AoE/range, & he doesn't seem aggressive nor intelligent enough to have a SUPER dangerous idea of "havoc", I'd bet. Still probably a contender for the most dangerous, though. The Lake Trio or The Creation Trio (among other possibilities.) need to get involved.
Rick Flag, US Special forces member & leader of the (DCEU) Suicide Squad? Like Rick Grimes, not that dangerous, but he might be a bit confused & alarmed being separated squad & a world full of (pocket) monsters. Can probably be handled by humans. Even if he decides to try catching Pokemon, there are probably better trainers, in terms of skill, ability to bond with Pokemon, etc.
Richard Watterson? Likely mistaken for a Pokemon, or some kind of bizarre humanoid, failing that. He is... intelligent. Unfortunately, I don't think the universal rules of plot present in TAWoG that prevent Richard Watterson from easily getting a job may not be present in Pokemon's world. So yeah, he probably causes yet another problem for Palkia &/or Dialga &/or Giratina &/or Arceus to fix.
Luckily, though, I think he's lazy enough that it wouldn't be IC for him to try to get a job, perhaps especially not, in this strange new world. Mr. Richard Watterson might have experience handling babies as a father in a family with 3 children should, but Baby Pokemon probably handle him handily.
Richard Spender? Probably feels right at home around Psychic, Ghost, & maybe some Fairy &/or Dark types, among others. Experience as a teacher dealing with the supernatural (Pokemon schools ARE a thing.) would be good if he wanted to adapt rather than just "sightseeing", but he probably gets bullied by babies.
Richter Belmont? Oh no, a Belmont. Much like Rick, who is Kirby's friend, The Lake Trio, or better yet, part of The Creation Trio (among other possibilities.) has to get involved to deal with him if he decides to stop sightseeing.
Nova (Richard Rider)? "Weaknesses: Rider uses the Xandrian Worldmind to help maintain his mood and mental stability. Without it, utilizing the full power of the Nova Force would overcome Rider's mental stability, causing a severe mental breakdown and possibly insanity."
Since the Xandrian Worldmind probably doesn't exist in the Pokemon universe.... How much of his powers work? In any case, he's probably an interesting matchup for Ultra Necrozma or other powerful Pokemon from Alola.
Richard Zeeman? Not much of a threat, probably able to be dealt with by humans.... Unless it's his Triumvirate Key. Then I guess you need Mew or Zygarde or some other Legendary or Mythical Pokemon or Ultra Beast to deal with him.
Richard Feynman? Unsure how his 4-C with Preparation works, but he can probably be dealt with by stuff from Alola. Or maybe by the Humans, since other than his Small Building Level Durability, he's a 9-C Human.
Dick Roman? For all his weird & horrifying abilities, a fully evolved Pokemon can probably handle him if he is 7-B. Otherwise he'd be a very tough fight, but still maybe possibly doable for a Baby Pokemon. I don't think his kind are welcome to sightsee as they please.
Pretty interesting thread! Looking forward to how it progresses!