The flight took Obama and Clinton from Washington to Charlotte for their first joint campaign appearance.
"There needs to be complete and timely transparency. Taxpayers deserve to know when, where and how much it costs when it comes to the use of Air Force One for political purposes," said Josh Stewart, deputy communications director for the Sunlight Foundation, a nonpartisan, nonprofit organization that advocates for disclosure and open government.
The labeling of the use of, and payment for, Air Force One has varied with past presidential candidates who have used the 747 for campaign travel. Obama and President George W. Bush identified their payments for the aircraft's use under a category other than "travel." In the 2012 filings for the Obama campaign, the use and payment of Air Force One was listed as, "reimbursement to travel offset account." In 2004, the Bush campaign listed the disbursements as "White House airlift operations." All of Hillary Clinton's plane expenditures during the campaign have been categorized as under "travel."
It costs $206,337 every hour Air Force One is in flight, according to a Freedom of Information Act letter obtained by the nonprofit Judicial Watch.
"When Air Force One is used to travel to a campaign event, the campaign has to reimburse the government for the pro rata share for each campaign traveler of what it would cost to charter a flight on an plane of sufficient size to accommodate all of the campaign travelers," said Larry Noble, general counsel of the Campaign Legal Center who also worked for 13 years as Federal Election Commission general counsel. "The reimbursement is done under government rules and must be reported by the campaign."
In a July interview with the FEC, deputy press officer Christian J. Hilland told CNBC: "If a federal candidate travels on a government-owned aircraft, including Air Force One, for campaign purposes, then his or her campaign committee must reimburse the government for the cost of the travel. ... The party or campaign committee that pays for the political or campaign-related expenses must disclose its payments on reports filed with the Federal Election Commission."
In a follow-up email to the FEC in light of the recent revelations, Hilland said: "I'd recommend you check with the White House. Candidates and representatives of political committees may make campaign travel via governmental conveyances, such as government aircraft, subject to specific reimbursement requirements. A political committee must reimburse the governmental entity providing the conveyance within the time frame specified by the governmental entity. A payment would appear in a committee's next regularly scheduled FEC report after the expense was paid."
CNBC asked the White House press office on Wednesday about the time frame for payment, but it referred the network to the Clinton campaign. In an email Thursday, a White House official said on condition of anonymity: "As in other Administrations, we follow all rules and regulations to ensure that the DNC or other relevant political committee pays what is required for the President to travel to political events."
The Democratic National Committee and the Treasury Department also didn't immediately respond to CNBC requests for comment Thursday about the billing and the deadline for payment.