Hi Hollie, that sounds like such a lovely project. This video shows how to make fabric roses easily - https://www.youtube.com/watch?v=Q9ncimRiXAo I'm sure it will work with drop cloth too.
Here's a drop cloth rose tutorial: https://www.craftberrybush.com/2013/09/drop-cloth-rose-tutorial.html
For a rug? You wanna make a rug out of drop cloth and add roses to it? You can find a drop cloth Rose tutorial here: https://www.craftberrybush.com/2013/09/drop-cloth-rose-tutorial.html
Hello Hollie! What a great idea! Check out some of the sites I have listed. Best wishes and Merry Christmas!!