I am not sure that anything fed at a volume of one cup maximum a day would have much impact on a horse in terms of hydration.
When I was looking at preventives for constipation impaction colic last winter, I did feed psyllium husks as one addition to the mash as they made things a bit more jelly like. But actually the key thing was total amount of water maresy drank, not what was added to the water. Flax also has a jelly like quality.
I am sure if chia seeds gave modern marathon runners a competitive advantage they would be in common use among athletes.
As JB pointed out a few comments upthread, the ration of omega 3:6 in flax and chia is similar, a bit better in flax but not necessarily enough to justify the cost.
When I look up fat levels, chia is 31 grams of fat per 100 grams, and flax is 42 grams of fat per 100 grams. Chia is 486 calories per 100 grams, and flax is 534 calories per 100 grams.
So the difference in both fat content and calories is not that much in relation to the overall diet of the horse. The nutrition values of both chia and flax are in the general range of other oily seeds.
Flax is a timetested supplement for horses, it is available locally, and it is cheaper than chia seeds. I don’t think I see any evidence that would make me think chia seeds would do something very different or better than flax.