Pierrick, 19, made his professional Palace debut in a clash with Norwich City in January 2020, going on to make two further first-team appearances that season.
He becomes the sixth Crystal Palace Development player to secure a loan move so far in 2021 – joining Rob Street, Ollie Webber, Nya Kirby, Scott Banks and Sam Woods.
Under-23s manager Shaun Derry said: "I'm delighted that Brandon has become the latest from our squad to secure a loan move and have no doubt that playing alongside professionals will help to develop him and his football greatly.
"Each of the lads who have been awarded loans in the last few weeks can see that hard work breeds rewards, and now it's up to them to make the most of these invaluable opportunities."
Pierrick added: "I’m buzzing to get started and I’m looking forward to impressing and showcasing my talent.
"At Palace, they prepare us for men’s football and I’ve been researching Kilmarnock before making the move here so I can’t wait to get to work on the training pitch and meet the rest of the group."