Flake had threatened to block Trump's circuit court picks without exception in order "to force a vote" on legislation in the Senate to limit Trump's protectionist trade policies.
Flake drew a distinction between Supreme Court nominees and circuit court picks in conversations with reporters on Thursday.
Flake said that he had informed his committee chairman that he would not vote for circuit court picks, yet "all the while I've been voting for district court nominees."
District courts are are "lower" and have the responsibility for holding trials. Circuit courts are appellate courts that only hear appeals for cases decided by the lower court.
Flake explained that blocking circuit court judges gives him "all the leverage I need."
As a member of the Senate Judiciary Committee, Flake's threat to block judges could have a significant impact on the confirmation of the Trump administration's appellate court nominees.
However, Flake, who is not seeking re-election, told the Arizona Republic that it was wrong to assume he would vote against everything Trump puts forward.
"There are lots of folks out there who assume because I've not been in line with lots of the president's policies, and certainly haven't condoned his behavior, that I should oppose everything, every one of the president's nominees or whatever," he said.
"I've never taken that position," Flake added.
Flake also told reporters he would approve Sen. Mike Lee, whose name is included in the list of 25 candidates from which Trump said he plans to select his next Supreme Court nominee, if Lee were picked.
"I think Mike Lee would be a great Supreme Court justice," Flake said."
Shortly after Kennedy announced his retirement on Wednesday, Trump said that the search for his second Supreme Court appointee will begin "immediately."