Probably not.
These are the things that make sense about each side:
Indication that he could do that: A remark about Kagutsuchi:
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As you can see he states: "It's almost certainly his left eye that controls amaterasu's black flames". I'd believe that if it could only control his specific amaterasu then it would have been paraphrased to show clarity and possibly hint towards it. Something along the lines of: "His left eye controls the amaterasu's black flames, created by the right eye". Then, again Kishi has made a lot of mistakes and he could have thought of the blaze release after he added amaterasu.
Indication that he can't:
This side would most likely be based the fact that the abilities made between two brothers aren't necessarily linked, they wouldn't be dependant to each other (Kakashi and Obito have the same set of eyes so, they wouldn't count.) Honestly, speaking if an amaterasu user could control another users flames regardless if they're related or not, it'd be pretty cheap.
So, this is just my opinion/view on this...(and pure speculation) the way it'd could be taken would vary from person to person.