Your soldier has to pay for his own travel back home during R&R when he is deployed overseas.
No, he does not. The military pays for this flight to the airport of his choice. The only stipulation is that whatever airport he flies into is the same airport he must fly back out of when he returns to theater.
Please note there is a scam where unsuspecting people are being told that a “soldier” must pay thousands to return home for R&R. The people are asked to wire money to the soldier to pay for his flight or he won’t be able to come home. This is a scam and not legitimate.