Coyle said: "We are happy to allow Adam to go out on loan to Accrington. We have a good relationship with the club and this will hopefully allow Adam to get some first-team football as the season comes to a close.
"We did a similar thing with Jay Rodriguez last season at Stirling and he really benefited from the exposure."
Stanley manager John Coleman added: "Adam is a promising youngster and we look forward to him joining the squad ahead of Saturday's game. We get on great with Burnley, Owen Coyle is a great friend of the club and we look forward to continuing the relationship."
Stanley have nine league games remaining in League Two and Kay could make his Football League debut in this weekend's home clash against Exeter at the Fraser Eagle Stadium.