I don't think you can use flax oil to make mayo, most use vegetable oil & what you do is put the eggs into a blender turn it on (with the lid on but the middle part out) & stream in the oil till it emulsifies. I guess you could put some flax in while you're doing this. The oil must be added slowly in the beginning until the emulsion is established.
Use 2 egg yolks & 1 whole egg, salt, pepper, lemon juice (2tbl), Dijon mustard and 2 cups corn, vegetable or olive oil (not too fruity). Put it in a blender & with the motor running add the oil in a slow steady stream. The eggs & oil s/b room temperature.
Voila! Mayo without all the chemical crap!!