I realize this is old, but it's bugging me :<
Looking at RedtheLEGEND's answer, it is correct for the most part. Affection, which you gain from a Pokemon from Pokemon Amie, is completely separate from friendliness. Pokemon Amie affection is used to get Sylveon, which would also require a fairy type move to be known by Eevee. For Umbreon/Espeon, the best way is to give it things such as proteins, berries, don't let it faint, etc. Otherwise, he is correct, a soothe bell would be a big help.