So I did some more research on this since there was a couple people curious, and the concern with chia seeds is the same as for flax. The main reason to supplement is usually for omega-3 fatty acids, but plant sources have short-chain acids, and we use long-chain acids. People convert these plant source omega-3's but dogs have limited ability to convert them to useable compounds, so if your primary objective is to supplement omega-3 (and not fiber source, pre-biotic etc) then you are better off supplementing a protein source omega-3 like fish oil.
One of the alternative medicine doctors on the board I use for information suggested using a coffee grinder to grind your own seed fresh daily so there isn't as much oxidation. Oxidation causes the oils to go rancid and actually makes them harmful instead of beneficial.