Is it a conflict of interest for a member of an architectural review committee in an H.O.A. to also be V.P. of the Association''s Board of Directors?

No not a conflict of interest unless ARC member has an interest in the outcome (maybe if they were a neighbor, or a competing contractor, etc.).  The board should address whether the ARC member can also vote on the appeal, but I doubt they have done that.  I think it is normal for at least one ARC member to be on the Board also.   This is specific to Florida law and does not constitute legal advice as the facts presented are anonymous and incomplete. This is intended for general education only and does not create an attorney-client relationship. This should not be relied on and you must seek your own attorney client relationship.