Fire Damaged Home Rebuilding Act of 2013 - Amends the National Flood Insurance Act of 1968 to allow local variances for certain residential structures substantially damaged by a fire or other disaster, not including a flood.

Permits state or local authorities, upon making certain determinations, to grant a variance from compliance with certain mandatory adequate land use and control measures to allow repair and restoration of an eligible structure to its pre-damaged condition without elevation of the structure.

Includes among such determinations that: (1) the repaired and restored structure will be located on the same site as it was before being substantially damaged, and (2) the number of floors of the restored structure will not exceed the number of floors of the original structure.

Restricts the maximum number of such variances to 10 during any calendar year.

Prohibits the Administrator of the Federal Emergency Management Agency (FEMA) from either: (1) finding that land use and control measures are inadequate or inconsistent with the comprehensive criteria for land management and use because they permit granting the variances identified under this Act; or (2) suspending an area or subdivision from participation in the national flood insurance program, or placing it on probation, because its land use and control measures provide for such variances.

Prohibits the chargeable flood insurance premium rate for a residential structure granted a variance under this Act from being lower than the rate that otherwise would apply if such structure had not been substantially damaged by a fire or other disaster (except a flood) and repaired and restored pursuant to the variance.