The length of the render function makes it difficult to know what all it's responsible for.
I broke out the wrapper <div>
into a small component, and the AgGrid row into a separate component.
I don't know how Flux works, but I'd make each of the user controls their own components. They can update the store as they do now (roughly, depending on how Flux does things like this) with results/etc still handled by the containing component.