The Collaborative International Dictionary of English v.0.48:

Influx \In"flux`\, n. [L. influxus, fr. influere, influxum, to
   flow in: cf. F. influx. See Influent.]
   1. The act of flowing in; as, an influx of light.
      [1913 Webster]

   2. A coming in; infusion; intromission; introduction;
      importation in abundance; also, that which flows or comes
      in; as, a great influx of goods into a country, or an
      influx of gold and silver.
      [1913 Webster]

            The influx of food into the Celtic region, however,
            was far from keeping pace with the influx of
            consumers.                            --Macaulau.
      [1913 Webster]

            The general influx of Greek into modern languages.
                                                  --Earle.
      [1913 Webster]

   3. Influence; power. [Obs.] --Sir M. Hale.
      [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

40 Moby Thesaurus words for "influx":
   accession, affluence, afflux, affluxion, augmentation,
   encroachment, entrance, entrenchment, impingement, imposition,
   increase, incursion, indraft, indrawing, infiltration, inflooding,
   inflow, influxion, infringement, injection, inpour, inpouring,
   inroad, inrun, inrush, insinuation, interference, interjection,
   interloping, interposition, interposure, interruption,
   intervention, intrusion, invasion, irruption, obtrusion, trespass,
   trespassing, unlawful entry