The flags didn't appear to hit Trump, and in video of the moment, he and Senate Majority Leader Mitch McConnell, who was walking alongside Trump, did not appear to stop.
The protester, who identified himself later to the press as Ryan Clayton, had been standing amid journalists gathered outside the meeting. Capitol Police swarmed him and removed him from the area.
Clayton is believed to be a member of the group Americans Take Action. He is thought to be the same person who tried to hand a Russian flag to Trump's son-in-law and senior adviser Jared Kushner when he appeared before the Senate Intelligence Committee in July.
Clayton was shouting about Russia, and at one point yelled, "Trump is treason!"
"Why are you talking about tax cuts when you should be talking about treason?" Clayton shouted at another point.
Trump was at the Capitol for a lunch to discuss policy with Senate Republicans.