Here is my take on the different main ships I've seen for Kakashi and Yamato and why they are all terrible except kakayama:
Kakashi/Iruka: bullshit. no one cares. Iruka is the definition of boring and he and Kakashi have nothing in common and no meaningful interaction. bye.
Kakashi/Gai: This is the definition of cheapening a close male friendship by making it romantic. Kakashi and Gai are good friends and they care about each other very much. Platonically. There is zero romantic chemistry.
Kakashi/Sakura: Gross. Stop it. Kakashi wouldn't date one of his students, and stop making poor Sakura your self-insert. This also goes for Kakashi/Naruto or Kakashi/Sasuke. I said stop it.
Kakashi/Obito: That's a big fat Nobito. They hated each other until like 5 minutes before Obito "died". Kakashi's posthumous relationship with Obito is guilt-driven, not romance-driven.
Kakashi/Minato: Damn, you people love these inappropriate relationships, huh? Kakashi was 14 when Minato died. They weren't in a romantic relationship. Knock it off. Also, Minato was his sensei. The power dynamic screams rape.
Kakashi/Rin: Sadly that was a one-sided attraction. Kakashi was like 13 when Rin died. There was nothing going on there. Also, Kakashi is gay so this goes for all heterosexual ships. Sorry.
Yamato/Iruka: How dare you. Have they even met? Because I don't think they have.
Yamato/Shisui: No, sorry. It isn't a thing. Every fic I've read with Shisui acts like he isn't even a shinobi. They definitely don't have compatible lives. Nah.
Yamato/Sakura: I thought I told you to stop? Besides, Yamato is also gay.
Kakashi/Yamato: These two have a rich, shared history of being saved by the other. Not only are their experiences as shinobi both parallel and complementary they both wield a kekkei genkai that they were not born with. Both struggle with the implications of that. On the same team in ANBU, on the same team as jonin, in the same bed as husbands. *chef's kiss*