GNU Collaborative International Dictionary of English

Found one definition

1.       
   Highflying (?), a.
   1. Extravagant in opinions or ambition. “Highflying, arbitrary kings.”  Dryden.
   
   [1913 Webster]
   
   
   2. Flying at a high altitude; -- of airplanes.
   
   [PJC]
   
   
   3. Having an excessively high cost or perceived value; temporarily very successful; -- of objects with respect to a market and people in their occupations; as, “highflying internet stocks; highflying executives moving between companies”.
   
   [PJC]