VA Appeals Modernization Act of 2016 This bill amends the Department of Veterans Affairs (VA) benefits appeals process to permit a claimant to request: a review of the Agency of Original Jurisdiction's decision by a higher-level adjudicator within the agency under which no additional evidence may be submitted; or a Board of Veterans Appeals (BVA) review under which no BVA hearing is requested and no additional evidence may be submitted or under which a BVA hearing is requested and the appellant requests an opportunity to submit additional evidence at, and within 90 days of, the hearing. ("Agency of Original Jurisdiction" means the activity which entered the original determination with regard to a claim for veterans benefits.) The BVA shall maintain two such separate dockets. A finding favorable to a claimant is binding on all subsequent VA adjudicators unless clear and convincing evidence is shown to the contrary. The BVA may remand a claim to the agency to obtain a corrective advisory medical opinion. The bill revises effective dates of awards provisions. The VA's duty to assist a claimant shall not apply: (1) once the claimant is provided notice of the agency's initial decision, and (2) to higher-level agency or BVA review. The VA is not required to send notice for a supplemental claim or to readjudicate a claim that has been disallowed except when new and relevant evidence is presented or secured (currently such provisions applies to reopening such claim). A claimants's notice of disagreement must set out specific allegations of error of fact or law. The BVA is authorized to dismiss an appeal which fails to do so.