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]

Moby Thesaurus II by Grady Ward, 1.0:

122 Moby Thesaurus words for "flier":
   Amtrak, Jehu, acrobat, aerialist, aeronaut, aeroplaner,
   aeroplanist, agiotage, air pilot, airman, airplanist, arbitrage,
   astronaut, aviator, baggage train, bareback rider, barnstormer,
   birdman, buying in, cable railroad, calculated risk, captain,
   chance, choo-choo, circus artist, cloud seeder, clown,
   cog railroad, cog railway, commercial pilot, copilot, crop-duster,
   el, electric, electric train, elevated, equestrian director,
   equilibrist, equity capital, express, express train, flutter,
   fortune, freight, freight train, freighter, funicular, gamble,
   goer, goods train, hazard, hell-driver, high-wire artist,
   horse racer, hummer, hustler, instructor, interurban, jet jockey,
   jockey, juggler, licensed pilot, lightning express, limited,
   lion tamer, liquidation, local, luck, metro, milk train, monorail,
   parliamentary, parliamentary train, passenger train, pilot, play,
   plunge, profit taking, racer, rack-and-pinion railroad,
   railroad train, rainmaker, rattler, ringmaster, risk,
   rolling stock, round trade, runner, scalping, scorcher, shuttle,
   shuttle train, sizzler, slack-rope artist, snake charmer, special,
   speculation, speed demon, speeder, spot sale, stepper,
   stockjobbery, stockjobbing, streamliner, stunt flier, stunt man,
   subway, sword swallower, test pilot, tightrope walker, train,
   trapeze artist, tube, tumbler, turfman, turn, uncertainty,
   underground, venture, venture capital, way train, wingman