Light fixtures

Hello, in my garage I have a single florescent light fixture. Its dark, I have some led light fixture ( hexagon style) I was wondering if I can just daisy chain off the hot, natural, ground wire going into the light fixture and running it to the led lights. Im not trying to led bulbs into a florescent fixture. The only reason is because its on a switch and I would have to run a wire down the wall or plug it into the ceiling and want a simple flip and it all comes on. For 1 kit its, 110v 240watts if that makes a difference. Also I bought 2 kits.