What is the orbital velocity of Pluto around the Pluto-Charon barycenter?
From the NASA Pluto Fact Sheet:

Mass of Pluto $m_1 = 1.303\times 10^{22}\ \mathrm{kg}$
Mass of Charon $m_2 = 1.586\times 10^{21}\ \mathrm{kg}$
Mean distance from Pluto $r = 19596\ \mathrm{km}$
Orbital period $P = 6.3872\ \mathrm{d}$

The orbit is nearly circular (the fact sheet gives an eccentricity of 0.0, other sources give very small values). So treat as circular motion.
The radius of the orbit of Pluto around the barycentre is given by:
$$r_1 = r \left(\frac{m_2}{m_1+m_2}\right) = 2126\ \mathrm{km}$$
Then use the usual formula for circular motion:
$$v = \omega r$$
where $\omega = \frac{2\pi}{P}$, giving a value of around $24.2\ \mathrm{m\,s}^{-1}$.