How can I tell AUCTeX that breqn is a math environment?

You can tell auctex about additional math environments using LaTeX-add-environments. For example, I sometimes use math environments named thm, prop, lem, cor, defn, not, rem, ex, notation, and equation*, and I tell auctex about them with the following lines in my .xemacs/init.el file:

(add-hook 'LaTeX-mode-hook 'add-my-latex-environments)
(defun add-my-latex-environments ()
  (LaTeX-add-environments
   '("thm" LaTeX-env-label)
   '("prop" LaTeX-env-label)
   '("lem" LaTeX-env-label)
   '("cor" LaTeX-env-label)
   '("defn" LaTeX-env-label)
   '("not" LaTeX-env-label)
   '("rem" LaTeX-env-label)
   '("ex" LaTeX-env-label)
   '("notation" LaTeX-env-label)
   '("equation*" LaTeX-env-label)))

Edit: In addition, here's some code suggested by thequark to have proper syntax highlighting for the dmath environment under auctex, plus a couple of other improvements:

(add-hook 'LaTeX-mode-hook 'add-my-latex-environments) 
(defun add-my-latex-environments () 
  (LaTeX-add-environments 
     '("dmath" LaTeX-env-label))) 

;; Code I added to make syntax highlighting work in Auctex 

(custom-set-variables 
 '(font-latex-math-environments (quote  
     ("display" "displaymath" "equation" "eqnarray" "gather" "multline"  
      "align" "alignat" "xalignat" "dmath"))) 
  '(TeX-insert-braces nil)) ;;Stops putting {} on argumentless commands to "save" whitespace 

;; Additionally, reftex code to recognize this environment as an equation 
(setq reftex-label-alist 
  '(("dmath" ?e nil nil t))) 

If you want the environment to be recognized by texmathp (used for instance by company-auctex), you can do it the following way.

(add-to-list 'texmathp-tex-commands '("breqn" env-on))
(texmathp-compile)