The Collaborative International Dictionary of English v.0.48:

flat foot \flat" foot`\, flatfoot \flat"foot`\ (Med.)
   A foot in which the arch of the instep is flattened so that
   the entire sole of the foot rests upon the ground; also, the
   deformity, usually congential, exhibited by such a foot;
   splayfoot.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

flatfoot \flat"foot`\ n.
   a police officer, especially a foot patrolman. [slang]
   [PJC]

WordNet (r) 3.0 (2006):

flatfoot
    n 1: a policeman who patrols a given region [syn: flatfoot,
         patrolman]
    2: a foot afflicted with a fallen arch; abnormally flattened and
       spread out [syn: flatfoot, splayfoot, pes planus]