My favourite red prop is a gigantic faded gold circus drum, with hand drawn red and white stripes on the percussion surface that are imperfectly perfect. It came from a dive of a second hand shop where the owners are true scoundrels with their pricing - as a poor student it was a bit out of my reach, I think it was $60, so Mum to the rescue giving it to me as an early birthday present.
Used against stark white, red I think it can look truly grand.
These pictures show how red doesn't always have to lead to the addition of Navy blue and therefore the much loved American flag look (which I too love). In these photos it looks delicate while still graphic and bold. A mistake would be to use a red pattern I think, but used in straight lines it looks classic and unexpected xx