Yes, you can
The Fey Teleportation feat (XGtE, p. 74) says:
You learn the misty step spell and can cast it once without expending a spell slot. You regain the ability to cast it in this way when you finish a short or long rest.
Since it says you learn the misty step spell, I would argue that you can then use it with other spell slots as well.
This is reinforced by the fact that it says "You regain the ability to cast it in this way...". If it was only intended to be a once per long or short rest ability it should have said "You regain the ability to cast it...".
Further evidence can be found by looking at the Magic Initiate feat (PHB, p. 168):
Choose a class: bard, cleric, druid, sorcerer, warlock, or wizard. You
learn two cantrips of your choice from that class's spell list.
In addition, choose one 1st-level spell from that same list. You learn
that spell and can cast it at its lowest level. Once you cast it, you
must finish a long rest before you can cast it again using this feat.
And this question about it from the Sage Advice Compendium v2.2 (p. 8):
If you have spell slots, can you use them to cast the 1st-level spell you learn with the Magic Initiate feat?
Yes, but only if the class you pick for the feat is one of your
classes. [...] In short, you must follow your character’s normal
spellcasting rules, which determine whether you can expend spell slots
on the 1st-level spell you learn from Magic Initiate.
This confirms that you can use spell slots to cast spells that you learn from feats, which is what happens in Fey Teleportation.
However this does also bring up the restriction that the spell, in this case Misty Step, would have to be on your class spell list in order to use it by using spell slots.
Additionally, prepared spellcasters would have to have Misty Step prepared in order to use it using slots.
Any other restriction or conditions of casting for your class also apply as normal.
This answer from the Sage Advice Compendium v2.2 (p. 3) suggests that maybe prepared casters would not be able to use these known spells as prepared ones:
If a druid takes the Magic Initiate feat and chooses detect magic as their one spell, can the druid cast that spell as a ritual?
A druid’s Ritual Casting requires a ritual to be prepared. The spell
from Magic Initiate is known but not prepared.
Rules designer Jeremy Crawford has confirmed that these feats work using the same ruling as MI in this unofficial tweet from December 2017.
Twitter user Isaac Leong asked:
How do the elven racial magic feats (Drow High Magic, Fey Teleportation and Wood Elf Magic) in Xanathar's interact with spell slots? They say that you know the spells and can cast them without expending spell slots, so can you use spell slots with them?
Another Twitter user, Armando Doval, replied:
You have to follow your class's Spellcasting (or Pact Magic) rules to cast a spell using spell slots (e.g. A wizard has to prepare the spell from their spellbook.) See "Magic Initiate" in Sage Advice Compendium https://dnd.wizards.com/articles/sage-advice/rules-answers-october-2017
I understand the wording is different. The part that's relevant is that you have to follow your class's spellcasting rules. Wood Elf Magic, etc don't say you learn the spell or that it counts as a spell for you.
If they didn't add "in this way" to those feats it'd sound like you can't cast them at all after using the feat. They're distinguishing the 1 use you get from the feat from other ways you might have to cast the spell.
Crawford confirmed this interpretation in a reply:
Your interpretation is 100 percent correct, @armando_doval.