Flat morphism

A morphism $f:Y\to X$ of schemes is flat at $y\in Y$ if the induced homomorphism of local rings

makes $\mathcal O_{Y,y}$ a flat module over $\mathcal O_{X,f(y)}$. The morphism is flat if it is flat at every point of $Y$.

Affine-locally, a morphism $\operatorname{Spec}B\to\operatorname{Spec}A$ is flat exactly when $B$ is a flat $A$-module. Flatness is local on both source and target.

Every field extension $K/F$ is a vector space over $F$, hence a flat $F$-module. Therefore $\operatorname{Spec}K\to\operatorname{Spec}F$ is flat.