You could use as a straight substitute for the normal oil, however as the Flaxseed oil is usually way more expensive...all you'd really need to use is several good tablespoons besides the regular oil per cup of mayo to get the benefit of the Flax.
Bear in mind, that if you plan to use Flax oil, don't use any cheap old veg. oil for the remainder in the recipe - add it along with a good quality Olive or Grapeseed or some other high Mono-Unsaturated Oil.