I have recently been diagnosed with celiac, so no wheat flour whatsoever. Also, I am allergic to corn.... I have read that arrowroot would not work in a roux; it is not just the thickening I want, but that flavor that a well browned roux has. Any alternatives?
A roux is a stable mixture (an emulsion) of fat and water held together by an emulsifier such as starch.
So you could try any number of flours from grains that contain starch such as potato, rice, barley, buckwheat, etc.
As far as the Maillard Reaction taste and color that you'd like to substitude, potato and barley (IMO) are the better bets. The note on arrowroot may be that it doesn't brown through the Maillard reaction.
An approach I would suggest is to use more than one flour/emulsifier and try to achieve consistency and taste by varying two or more ingredients as opposed to a direct single substitute. This may also mean that you'd likely have to the color/taste/browning first and then bind it to achieve the final result.
Have a look at Bob's Red Mill's list of flours and experiment. A little bit of Hazelnut flour and you might never look back at an ordinary wheat flour roux again.