Earlier in the same dictionary, Partridge has this entry for cracking as an adjective:

cracking, adj. Very fast ; exceedingly vigorous (-- 1880) : slightly ob[solete, in 1936]

By the fifth edition (1961) of the dictionary, however, Partridge had evidently rethought the place of “get cracking” in the larger scheme of similar phrases and had adopted the entry that ghoppe reports in a different answer here, with the suggestion that it might have its origin in “whip-cracking at the mustering of cattle.”

Early Google Books matches

Google Search results generally support Partridge’s1936 reading of the phrase. The earliest relevant matches are from 1938, and one of them is RAF-specific. From Popular Flying, volume 6, issue 9 (1938) [combined snippets]:

We've got a new vocabulary in Black Bourton, the vocabulary of the R.A.F. Nice things are "wizard"; nasty people are "ropey types," and a reckless man is "split." One is "browned off" when one is rather depressed; the ground is the "deck" and the sky is the "ceiling"; dull-witted people are "drips," and when in a hurry we ask each other to get "cracking." This strange lingo is, of course, subject to changes and ex-R.A.F. men of several years ago would find themselves hopelessly dated by the expressions they use.

There is, however, one outlying instance of “got cracking”—or more precisely “got cracking away”—that might be significant s well. From Bertram Milford, In the Whirl of the Rising (1904), a novel seemingly set in Rhodesia during the Second Matabele War, of 1896–1897:

"You must have had the very devil of a scrap, Peters." one of these [horsemen from Green's Scouts, a relieving force] was saying. "We could hear you banging away from the time you began, and pushed our gees for all they'd carry; for we reckoned all that shooting meant a big thing and no bally skirmish. ... They [the Matabele forces] didn't know we were there till we got cracking away right in their faces, or mostly backs. Magtig! Didn't they skip. …"

BEAUTIFUL

What happens when criminals run their gangs from prison?

What happens when putting criminals to death does not stop the crime?

How do you imprison the soul?

How do you measure talent?

The first assault was on my sleep cycle.
NO
…with the help of a god?
I didn’t sleep for 6 months.

The second assault was on my digestion.
They felt justified.
This second assault is permanent and has cost insurance underwriters MONEY. That’s money to you.

The third assault was covered with bull horn talking in the street and news.
There were many people talking.
There are people exulting.
Do I have cancer?
Sisal Chabash directs me to continue on normally. When will I die? I will, but that is her concern.

Thank you Jesus!