Have never made these , but maybe if you can tell us a little more about your project someone could help. how big are you makeing the flag, and what you are useing it for? and any photos would help. sorry I cant be much help.
Happy Crafting
oddie

You can do it either way but traditionally, yo-yo quilts didn't have a backing. Yo-yo quilts are actually coverlets and were just laid across other bedding.

How big is your flag and what do you plan to do with it? Whether or not you need backing may depend on your plans. Yo-yo quilts and other items made by joining them, don't hold up incredibly well so if they are large and you plan to hang it somewhere, it will pull at the seams. They do require a lot of fixing over time.

I started making a quilt about two years ago. I posted pics this fall of my progress..I was up to about 1000 yo-yo's. I haven't touched it in a few months because I grew tired of it. I'll pick it up one day and get back into it, I'm sure but for now, it's laying on the bench at the foot of my bed :)

I am doing a small one - my circles are 7 inches. Thinking 2 or 3 across and 2 or 3 down for the stars, then red with tiny white stars for the red stripe, and white with tiny blue stars for the white stripe. The stars are a navy background with bigger white stars. Thinking I might put it in a frame (without the glass, of course).

You wouldn't need a backing then. The yo-yo's will hold up just fine in a frame because they'll be attached to the whatever you use for the backing there. A smaller item like that won't have as much trouble as say a quilt for a bed.

When you say 7" you mean prior to making the yo-yo, correct? When you are reading about yo-yo sizes, they usually measure them after they are made :)

Good luck!