I have to give the unsatisfying “origin unknown” for this one. It can be traced to American slang usage from the Civil War period, but it may be considerably older and possibly not American in origin. From The Agitator of Wellsboro, Pennsylvania of 12 January 1860:
You’d oughter seen that gang skedaddle.
The first citation in the Oxford English Dictionary is from some 18 months later in the New York Tribune of 10 August 1861:
No sooner did the traitors discover their approach than they “skiddaddled,” (a phrase the Union boys up here apply to the good use the seceshers make of their legs in time of danger).
It is sometimes said to be of Swedish or Danish origin, but there is no evidence for this. It may be from English or Scottish dialect, but the evidence for this is scanty. From the Atlantic Monthly of January 1877:
But my English friends lost no time in upsetting my hypothesis “Why,” they exclaimed, “we used to live in Lancashire and heard skedaddle every day of our lives. It means to scatter, or drop in a scattering way. If you run with a basket of potatoes or apples and keep spilling some of them in an irregular way along the path, you are said to skedaddle them. Or if you carry drops of milk on the stair-carpet, to mark your upward course and awaken the ire of the housekeeper, you are said to have skedaddled the milk.”
Copyright 1997-2013, by David Wilton