The Collaborative International Dictionary of English v.0.48:

Flier \Fli"er\ (fl[imac]"[~e]r), n. [Form Fly, v.; cf.
   Flyer]
   1. One who flies or flees; a runaway; a fugitive. --Shak.
      [1913 Webster]

   2. (Mach.) A fly. See Fly, n., 9, and 13
      (b) .
          [1913 Webster]

   3. (Spinning) See Flyer, n., 5.
      [1913 Webster]

   4. (Arch.) See Flyer, n., 4.
      [1913 Webster]

   5. An a["e]roplane or flying machine.
      [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

flier
    n 1: someone who travels by air [syn: flier, flyer]
    2: someone who operates an aircraft [syn: aviator, aeronaut,
       airman, flier, flyer]
    3: an advertisement (usually printed on a page or in a leaflet)
       intended for wide distribution; "he mailed the circular to
       all subscribers" [syn: circular, handbill, bill,
       broadside, broadsheet, flier, flyer, throwaway]