Unknown, but she probably went back to Mirkwood
Tauriel is an original character in the Jacksonverse, and only exists within it. No authoritative information about her fate after the Battle of Five Armies has been revealed.
However, in a 2014 interview with Hero Complex1, Tauriel's actress Evangeline Lilly gave her thoughts, for however much value you ascribe to actor opinions (italic is their emphasis, bold is mine):
HC: What do you think happens to [Tauriel] after the events of “Five Armies”?
EL: You know, it's going to sound very mundane, but I think she goes back to Greenwood — which would hopefully now be Greenwood; slowly but surely it would evolve out of Mirkwood and return to Greenwood — and she goes back to work. It sounds so boring, but ultimately, she has a job. She has a responsibility. She’s the head of the Elven Guard. She's not head of the Elven army — that is Prince Legolas and King Thranduil — but she's the head of the Elven Guard, and they protect their realm. And maybe she doesn’t go back to being head of guard, maybe she's been softened and wouldn't resume her old position, but in a way I feel like maybe she would be even more impassioned to protect what she loves, to protect her home, to protect what's important to her, but maybe she'll do it now with more compassion and a little bit of softness.
If that's the case, then Tauriel would have been busy defending Mirkwood against the attack that happened there
1 The Entertainment/superhero division of the Los Angeles Times