How do we calculate the escape velocity of galaxies?
In short, the escape velocity from the region we find ourselves in the milky way is 544 Km/s +- 10%.

This number, and an extensive explanation of how it was calculated can be found on a paper called The RAVE Survey: Constraining the Local Galactic Escape Speed

Also important to consider is the fact that we already are at aproximately 220 Km/s because of the sun's orbital velocity, so the actual value needed to get there from earth is much lower.