Does it mean "a warning sign"? "The economy slows as consumer spending, which makes up the majority of U.S. economic growth, flags." Source: http://money.cnn.com/2017/10/19/news/economy/inflation-economy-mystery/index.html?iid=SF_LN
No, "flag" in that situation means "to lose vigor or strength; to weaken or to diminish". The consumer spending is flagging, so it's diminishing. For example:
"Our conversation began to flag as the hours went by."
This means that our conversation began to lose its strength or diminish; we weren't talking so much in the sixth hour as we were in the first hour.
NOTE: This use of "flag" as a verb, which has an etymology different from the word "flag" like the "American flag", is fairly uncommon. You will almost never see or hear it used except maybe on TV news channels like CNN or in formally-written material; no one says it in conversation; at least, I can't remember hearing it. I know its meaning only because I've read it in books, newspapers, and magazines before. I have heard it used as an adjective before in the phrase "a flagging economy".