I decided to run a Google Books search for "flipping through the news" to see how many of the matches would be part of the longer phrase "flipping through the news channels." To my surprise, Google Books found only four matches for the shorter phrase—and in all four instances the author was actually using the longer phrase. Here are those four occurrences. From The Believer, issues 5–8 (2003), page 102 [combined snippets]:
BLVR: Satirists tend to thrive during periods of national instability. If we're perfectly content with our politicians and the world is one big happy place, there's really no point in mocking any of it. What's bad for the nation is good for the comedy writer. Do you ever find yourself flipping through the news channels and hoping for something horrible to happen? Not on a 9/ 1 1 scale, of course, but at least something absurd or infuriating enough to get your satire mojo working.
TF: No. Never.
From Jane Berentson, Long Division: A Novel (2010):
Cracking an egg in a skillet.
Eating clams with Gus.
Letting the phone ring and ring.
Laughing with Loretta.
Flipping through the news channels on my television.
From Joyshri Lobo, Bartered Lives: Love and Betrayal in North India (2014):
A mountain range and many borders away, Commando sat flipping through the news channels. Another attempt had been made to assassinate the President of Afghanistan, Hamid Karzai. He escaped but many of his security guards were killed or wounded.
And from Suhas Inamdar, Life Version 2 (2016):
Abhijeet asked him, "Yes Narayan, tell us, on which news channel did you see this person? What was the news about?"
Narayan said, “Sir, yesterday evening, as I was randomly flipping through the news channels, I happened to see a news about this person being arrested on charges of committing fraud. I could not see the full news, but I could make out that he was arrested for some fraud case."
The alternative expression for news in print appears to have been not "flipping through the news," but "flipping through the newspaper" or "flipping through the pages of [a newspaper]." A Google Books search finds matches for the former expression from 1972, 1976, 1977, and later.
From a chronological perspective, "flipping through the news channels" may have been easier for English speakers to adopt because they were already familiar with the expression "flipping through the newspaper"—even though news channel flipping is figurative whereas newspaper page flipping is literal—but I don't find evidence in Google books that the exact expression "flipping through the news" antedated "flipping through the news channels" or that it was ever a common short form of "flipping through the newspaper."
Update (December 9, 2016): 'flipping through the news' vs. 'flipping through the channels'
Following up on a comment by Hot Licks from October 9 of this year (beneath the poster's question above) that "I suspect that 'flipping through the channels' is far more common," I ran a Google Books search for "flipping through the news" (blue line) versus "flipping through the channels" (red line) for the period 1950–2005, which yielded this chart:
This result confirms Hot Licks's suspicion and is consistent with my finding (discussed above) that all four matches for "flipping through the news" in Google Books search results involved the longer phrase "flipping through the news channels."