Luton have made their ninth summer signing following the arrival of winger Danny Green.
Notts County have signed Togo international Mawouna Amevor on a two-year deal.
Teenagers Crawford, 18, and Shankland, 17, and 22-year-old Sinclair will all travel to England on Monday and will stay until Thursday.
Ayr, who are a part-time club, confirmed that the trio would be due back by next Saturday ahead of their game at Brechin City.
Honest Men boss Mark Roberts told the Ayrshire Post: "We've also had clubs such as Bolton, Crystal Palace and Charlton at our games this season and it underlines that the Academy is doing a great job.
"Crawford and Sinclair are there on merit while Shankland is going due to his reputation since a boy.
"It's a great chance to train and learn. They are all aged under 23 so if anything comes from it, there could be good money for Ayr."