Fair Local Adjustment for Tenant Rents Act of 2014

Fair Local Adjustment for Tenant Rents Act of 2014 - Amends the United States Housing Act of 1937 to revise and eliminate specified requirements with respect to public housing agencies (PHAs) establishing flat rental amounts for PHA dwelling units.

Authorizes a PHA to request the Secretary of Housing and Urban Development (HUD) to establish a flat rent for a dwelling unit in an amount less than the required 80% of the applicable fair market rental, if the PHA demonstrates that such minimum amount is not an accurate measure of the unit's rental value.

Changes $50 from a maximum to a minimum monthly rental amount (including utilities) for individuals: (1) residing in public housing, (2) receiving tenant-based rental (voucher) assistance, or (3) receiving tenant-based assistance under the certificates or moderate rehabilitation programs.