Hi K.,
I patch all of my girls' jeans that I possibly can. It's not just Old Navy jeans that do this. It's also Arizona's and Silvertab, Faded Glory, Osh Gosh--EVERYTHING. You CAN'T avoid it. Don't waste the money on buying specific brands. It's just not worth it. Kindergarten age kids are on their knees CONSTANTLY and thus have holes wear thru almost immediately.
Walmart used to carry a standard denim patch, but all of our area stores have since stopped dealing w/ crafts (a huge mistake on their part for this area for sure!) but I've also found them at Jo-Ann Fabrics. I will take one of the denim patches and cut into little hearts for my girls and then just iron it on. Then I will secure it by handstitching around the outside. I've allowed some patches to go free, but then you need to keep ironing over the patch after so many washings. However, if your son isn't comfortable w/ wearing an iron on patch of some sort, do it on the inside. You must be careful though, and refer to your school's handbook on dress code. Our school district will NOT allow ANY frayed or holey clothes AT ALL. All holes MUST be covered somehow.
A word of advice for you though--don't just assume that because he's never been thru a growth spurt before, that he won't start. We never went through big ones here until about first grade w/ our older one. She's currently in 3rd grade and is in her 2nd entire wardrobe since August, soon to be her 3rd because she's gaining so much height. She's done this to us the last 3 school years. All I can say is that I'm glad I have her clothes to hand down to her twin sisters. I couldn't afford to have all 3 doing that at the same time :)
Best of luck to you and Happy New Year!
E.