I doubt there are any laws about it so just look around your area to see what others are doing.
For my area, the service patch is on the left, and an American flag is on the right. Both patches are as desired. Most people forgo the flag, and the trend now is to get a embroidered department logo on the left chest and forgo all patches entirely.
Once again, YMMV depending on standards in your area, but you can't really go wrong as it's your department, your rules.
Addendum, actually you can go wrong, please avoid the temptation to put 10 patches on your uniform. We don't have a state patch here, but I know some states require it, so that's fine. But that, an your department patch should be more than enough. Unless it's mandated by someone, there is no reason for other embroidery, badges, bells, or whistles (figuratively or as I saw in one case, literally... It made knowing when this private company's EMTs were walking behind me in the hospital very easy!)