Primitive-module flatness conjecture for additive-type group schemes

Let $A$ be the base ring and let $G\in\operatorname{Gr}^{+}_{A}$ be a group scheme of additive type. Write $G=\operatorname{Spec}(B_G)$ and let $\operatorname{Prim}(B_G)$ denote the module of primitive elements of its affine algebra. Primitive-module flatness conjecture. The $A$-module

$$\operatorname{Prim}(B_G)$$

is flat.

This is identified as the first difficulty in extending the theory from finite to infinite group schemes. The conjecture is open in the stated generality and would provide the required flatness for the primitive-element construction.