Does minotaur reckoner prevent units from moving back to base with spells like ride the wind or flash?

Yes — Minotaur Reckoner's restriction applies to all moves to base, including spell-based moves like Ride the Wind and Flash.

You can still legally play Ride the Wind or Flash, and the spell resolves — but on resolution, the move instruction is simply ignored because it can't be followed (Rule 359.3.e.6). The unit stays where it is. If the spell has other independent instructions (e.g., Ride the Wind's "ready it"), those still resolve as normal.

Note this is different from Vilemaw's Lair-style "can't move to base" — it's the same principle in reverse: the restriction doesn't stop the spell from being played, it just makes the move fail.