The spell description is very clear on the glowing:
Each object in a 20-foot cube within range is outlined in blue, green, or violet light (your choice). Any creature in the area when the spell is cast is also outlined in light if it fails a Dexterity saving throw. For the duration, objects and affected creatures shed dim light in a 10-foot radius.
Any attack roll against an affected creature or object has advantage if the attacker can see it, and the affected creature or object can't benefit from being invisible.
There is no special exception for hiding or visibility. If you are in the range of the spell's effect, you make a Dexterity saving throw. If you fail it, you are outlined in light.
Whether or not you can hide, and how well, are up to the DM:
The DM decides when circumstances are appropriate for hiding. When you try to hide, make a Dexterity (Stealth) check. Until you are discovered or you stop hiding, that check's total is contested by the Wisdom (Perception) check of any creature that actively searches for signs of your presence.
You can't hide from a creature that can see you clearly, and you give away your position if you make noise, such as shouting a warning or knocking over a vase. An invisible creature can always try to hide. Signs of its passage might still be noticed, and it does have to stay quiet. (PHB, Chapter 7: Using Ability Scores, Using Each Ability, Dexterity, Hiding)
So whether or not glowing would reveal you depends on the scene overall and how you are hiding. If you are hiding in a closed, lightproof box, then the glowing might not matter at all. If you're hiding by ducking into a dark corner, suddenly starting to glow might automatically reveal you without an observer needing to make a roll. Crouching behind a low wall might produce a faint glow which a potential observer could roll Perception to notice (or notice with Passive Perception).
The Cloak of Elvenkind doesn't necessarily matter. It gives Advantage on a roll to hide, but the result of that roll is the result of your effort to hide. It imposes Disadvantage on Perception checks made to notice you, but the result of that roll is the result of that effort. If circumstances make hiding impossible, like suddenly glowing in the dark (as above), then you can't hide.
The argument that hiding might make it impossible for an observer to see you is a decent one. But if the observer knows how Faerie Fire works, and knows it's been cast on an area where you might be, suddenly seeing dim light centered on a particular spot is a pretty good argument that that spot is where you are. In such a case, you may still be unseen, but not necessarily hidden.