There is no tax reason why a multimember LLC could not engage you as a subcontractor. Your LLC income is reported on a 1065 and K-1, and the subcontractor income would be on a schedule C as part of your personal tax return.
The question should be directed to the other members of the LLC and your (hopefully written) partnership agreement. You would be shifting part of the income exclusively to yourself. Is that a conflict of interest? Is it allowed by the partnership agreement? Would your partners approve? If you have a partnership agreement, what did you each bring to the table, and why are these particular skills or tasks not part of your participation under the agreement, why are they something extra?
I don't think the IRS will care as long as you pay your taxes. But your other partners might have an interest in the matter.
