J. E. Lighter, Historical Dictionary of American Slang

ball the jack1. To go fast (said esp. of a railroad train), make haste, ....

1913 Jim Burris & Chris Smith Ballin' the Jack (song) [ragtime]; Now that's what I call "Ballin' the Jack."
1914 in Handy, Blues Treasury 74: Said a black headed gal makes a freight train jump the track / But a long tall gal makes a preacher ball the jack.

1918 in Niles, Singing Soldiers 25: I come to France to make the Kaiser ball de jack.

In other words, a railroad term for traveling fast, but borrowed for other uses.