Not sure whether I should put the patch on and if I do where should I place it. What are y'alls thoughts?
You can put it above your chest pocket (close to the heart, if ya feel patriotic), but that's a bit overplayed and it's going to ruin some symmetry.
Personally, I would put it on your upper back just below the neck and the collar. Denim jackets tend to have a rectangle there.
Next time post in DIY general please.
It's aight, I wouldn't do it myself (second sleeve without patch would stick out too much IMO) but it's not a bad idea.
Generally speaking you always want to place a patch somewhere near the pockets, arms or your back.
The exception is when you want to make a battle jacket.