I love them as nicknames but they seem a bit incomplete singularly. Not sure why since I love one-syllable names... but these just don't work as well.
Though,
Jem is kinda cute and reminiscent of Gem,
Gemini.
Frey makes me think you meant to say
Freya, but I do like the sound a lot.
I always thought that
Linnea would be an awesome twin name as it is a twin flower.
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Mama to my pretty Nin (Nadine Marikit) and my Clarybee (Clarisse Bituin). Mahal na mahal from our little family to yours!