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In The Civil War: a Narrative, Shelby Foote periodically uses the phrase "airline miles" to mean "distance on a straight line." I can't recall offhand hearing this phrase anywhere else; why this phrase?
Commercial air travel was still fairly new then. The first volume was published in 1958, the same year as the introduction of the Boeing 707, which was the first commercially successful passenger jet. Was that an influence at all?
This is the original sense of the word airline. Now obsolete, it survived in works on surveying and military history into the 1960s. The OED says:
airline, n. 1. a. Chiefly U.S. A direct line through the air; a straight line between two points on the earth's surface.
with citations dating back to the early 19th century:
1829 J. F. Cooper Wept of Wish-ton-wish ii. 27 This clearing, which by an air line might have been half a mile from the place where his horse had stopped.
1852 G. Grote Hist. Greece IX. ii. lxx. 160 If we measure on Kiepert's map the rectilineal distance, the air-line is 170 English miles.
The OED's earliest citations for the sense "air transport service" are from 1890.
