Linearity theorem for flat affine group schemes

Let $S$ be a scheme. A linear group scheme over $S$ is a group scheme $G\rightarrow S$ that, locally in the étale topology of $S$, embeds as a closed subgroup scheme of $GL(E)$ for a finite-rank vector bundle $E$ over $S$. Linearity theorem. Every flat affine group scheme of finite type $G\rightarrow S$ is linear. This is presented as a standard fact used to extend cohomological results to coefficient stacks involving flat affine group schemes; the source gives no further discussion of its proof or attribution.