Production process of kevlar
From this Wikipedia page:  


  Kevlar is synthesized in solution from the monomers
  1,4-phenylene-diamine (para-phenylenediamine) and terephthaloyl
  chloride in a condensation reaction yielding hydrochloric acid as a
  byproduct. The result has liquid-crystalline behavior, and mechanical
  drawing orients the polymer chains in the fiber's direction.
  Hexamethylphosphoramide (HMPA) was the solvent initially used for the
  polymerization, but for safety reasons, DuPont replaced it by a
  solution of N-methyl-pyrrolidone and calcium chloride.


The structure of Kevlar is given from the same page:  

  

However, Kevlar production on a small laboratory scale will likely be an expensive and difficult endeavor compared to purchasing Kevlar products, which are available in about any form you can imaging, many of them patented. Also, as Kevlar is water insoluble, concentrated sulfuric acid is required to keep it in solution during synthesis, molding, spinning, etc.  Good luck ;)