The American flag is in the public domain. Therefore, the American flag is not the subject of copyright or trademark. Therefore, if your decal is not a modified version of American flag, you can put it on your product and sell the product.
You can have trademark rights without registering your trademark. Those unregistered rights are sometimes referred to a common law trademark rights.
To check to see if you may be infringing, you would need to check federal, state and common law trademarks.
the mere fact of have an LLC name registered with your state's Secretary of State does not protect you against infringement.
A starting point may be to search whether your logo might infringe another's logo. If it does not infringe, and you want to register your logo without the help of an attorney, go the the US trademark office to complete a trademark application - https://www.uspto.gov/trademarks-application-process/filing-online
You can have trademark rights separate from registration