Flabébé, Floette, and Comfey can learn Vine Whip by Level-Up.
To be honest, the way the moves have types and how they are... some make sense while others don't.
What does make sense is my headcanon of it (or at least a theory).
My theory is that each attack has aura on it, no matter the attack. The Shadow Moves from the Colosseum and XD games shows that the Shadow Rush and other Shadow-Type attacks are corrupted attacks, attacks with the Shadow aura. Because of this, other attacks must follow the same basis. Grass aura is used for Grass-Type attacks, Fairy aura for Fairy-Type attacks, and Dark aura for Dark-Type attacks (further emphasized by the Fairy and Dark Aura Abilities, as well as Aura Break, by the XY Legendary Trio: Xerneas, Yveltal, and Zygarde). Plus, aura is a very integral part in Lucario and the Mystery of Mew, among other media.
This also explains why other Pokemon are the types they are when they so obviously need the other typing (like Golduck not being Psychic-Type). They have an affinity to certain types, while they are that type. Their aura is the basis of who they are, while also giving them the affinity (as well as their body biologically) to use certain moves. This also explains how Zoroark, a Pokemon unable to use any Fire-Type moves and has no organs to do so, can learn Flamethrower. They manifest their aura into Special attacks or they manifest their aura on a body part for Physical attacks. There are some attacks that don't need the aura (like Rock Throw or Tackle). These are rudimentary attacks that don't need the aura. Most Normal-Type attacks that aren't too strong don't need the aura. Moves like Hyper Beam, Giga Impact, and Trump Card use aura.
Otherwise, Vine Whip would indeed be a Normal-Type attack or do little damage.
