Whisk the gelatin, corn syrup, vanilla, and salt with 1/2 cup boiling water until the gelatin dissolves.
Start beating in the confectioner's sugar some at a time until a soft sticky dough forms. Have some extra powdered sugar (as much as 1-2 cups or maybe more) handy, and start kneading the dough together, adding extra sugar as needed.
Knead for several minutes until the dough is smooth and no longer sticky.
Divide the dough (using a bench scraper or chefs knife) into as many pieces as the number of colors you want to end up with.
Working with one piece at a time (cover the others in plastic wrap), add 2-3 drops of food coloring and knead until the color is evenly distributed and nicely pastel colored. You can also add a drop or two of extract flavoring before this kneading step.
Take a piece of parchment paper and lightly coat with cooking spray. Roll out each piece of colored dough until it's maybe 1/8 - 1/4" thick, and then cut out hearts (of whatever size you like). I found it easiest to take the rolled out dough and place directly onto the parchment and then cut out the shapes, removing the excess dough around the hearts. This way, you don't have to transfer cut hearts from one surface to another, a process which can render the surfaces imperfectly smooth.
Take the dough trimmings and re-roll as many times as you need to keep cutting out more hearts.
You can imprint messages into each heart at this stage with small letters. Otherwise, leave them out to dry at room temperature overnight before writing messages onto them with food decorating pens.