Alzheimer's Accountability Act of 2014 - Amends the National Alzheimer's Project Act to require the Director of the National Institutes of Health (NIH), for each fiscal year through FY2025, to submit to the President for review and transmittal to Congress, after reasonable opportunity for comment (but without change) by the Secretary of Health and Human Services (HHS) and the Advisory Council on Alzheimer's Research, Care, and Services, an annual budget estimate (including regarding personnel needs) for the NIH initiatives under the Act.