Boocock, 18, scored twice in the first half to put Frickley 2-0 in front, but they surrendered to a Tyler Blake hat-trick and were beaten 3-2 by Carlton Town.
Manager Craig Spink said: “We are delighted to have Rieves with us on loan from Doncaster Rovers.
"He’s an exciting young talent with bags of potential and was prolific in the DRFC youth team last season. He’s quick, scores goals and can play in a number of attacking areas."
He replaces Rian McLean, who has returned to Doncaster following a similar loan spell.
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