How Much Length Can a Veneer Add to Canine Teeth?

From the picture that you provided it seems that you could add some length back to your canine, but I am not sure about 3mm.  You are limited on the length of your canine based on how your lower jaw moves when you move it side to side.  I would consult with a cosmetic dentist and let them assess just how much length can be added without risking fracturing the veneer.  Good luck.

But there are limits to how long.  SOME people can add 3 mm, but most people have bites that limit how long the teeth can be.  

From your photo, you display some flaring of teeth, which may indicate that the lower jaw pushes extra hard against the upper teeth.  This MAY mean that you exert forces that a long veneer can't survive (you report that the canine did chip previously).

You would benefit from an office that can thoroughly evaluate your bite before you start any treatment.  Often, this requires sophisticated computer equipment for complete accuracy (K7 from Myotronics, JVA from Bioresearch or a Tek scan).

It does appear that your canines are too short. Sadly you cant get your enamel back but you can do bonding or veneers on those canines. When you slide your teeth from side to side your upper and lower canines should slide up one another. Canine guided bite is what is optimum.