Whisk the gelatin, corn syrup, vanilla, salt and 1/2 cup boiling water in a stand mixer bowl until the gelatin dissolves. Using the paddle attachment, beat in the icing sugar on medium-low speed, 1 cup at a time, to make a stiff, sticky dough.
Transfer the dough to a clean surface and knead, adding more icing sugar as needed (up to 1 cup), until the dough is smooth, pliable and slightly tacky, about 5 minutes.
Divide the dough into 4 pieces. Flatten 1 piece into a disk. Cover the rest with plastic wrap. Add a few drops each of food colouring and extract to the center of the dough; fold in the sides and pinch closed, then knead until the colour is distributed.
Lightly coat a large piece of parchment paper with cooking spray. Roll out the coloured dough on the parchment until 1/8 to 1/4 inch thick. Cut into hearts using 1-inch cookie cutters; transfer to a parchment-lined baking sheet.
Repeat with the remaining dough, using different colours and extracts. Let the hearts sit at room temperature, uncovered, until dry and hard, about 24 hours, flipping them halfway through.
Write messages on the hearts using food decorating pens. Store in an airtight container for up to 1 week.