I looked it up!

    "Given a recent estimate of 4.3 million solar masses for the
    mass of Sagittarius A* and S2's close approach, this makes
    S2 the fastest known ballistic orbit, reaching speeds
    exceeding 5000 km/s (11,000,000 mph) or 1.67~% of the speed
    of light and acceleration of about 1.5 m/s2 or almost
    one-sixth of Earth's surface gravity.[7]"

https://en.wikipedia.org/wiki/S2_%28star%29

Edit: wait that's not it, that's S0-2, but you're talking about S14/S0-16:

https://en.wikipedia.org/wiki/Sagittarius_A*#Central_black_h...

From those parameters, its perihelion speed would be about 8,200 km/s (2.7% c), using the classical approximation.

https://en.wikipedia.org/wiki/Perihelion#Mathematical_formul...

Interesting tangent: when there's a binary star system that gets very close to this black hole, the three can interact in a way that one of the two stars falls in, while the other steals its gravitational potential and is ejected at extreme speed. There's a few "hypervelocity" rogue stars in the Milky Way, which were probably accelerated by the black hole. They're on escape trajectories leaving the galaxy.

https://en.wikipedia.org/wiki/Stellar_kinematics#Hyperveloci...

https://en.wikipedia.org/wiki/HE_0437-5439

Wow thank you for the second link. That was really interesting read.