No, it is not grammatically correct. Since scintilla is feminine (and since arcanus, -a, -um is one of those adjectives that have special endings in the feminine gender), it should be arcana scintilla vitae.
The same applies to your second phrase; it should be mystica essentia vitae.
Other than that, both suggestions look quite good to me.
I googled a bit, and scintilla vitae is clearly a time-honoured phrase, although it is not clear to me how old it really is. It is, however, reminiscent of the scintilla animae (spark of the soul) of the late medieval German mystic Meister Eckhart. Essentia vitae, on the other hand, seems to be an old (18th, 19th century) pharmaceutical term for certain mixtures; I would not let that deter me, though: essentia clearly means "essence" in the philosophical sense first, and in the, shall we say, snake-oil sense last.