Yep, the rule was, you had to sit during the anthem...UNLESS the flag salute came first, and since you were already standing for that out of respect...
In public school, I complied and it sometimes made me a target of teachers. I often tried to avoid being anywhere where this might come up, if I could do so. For instance, rather than attend a pep ralley, I sat outside the gym and read a book.
None of these rules made sense to me even then. I could not effectively explain to myself why I had to sit during the anthem, but stand during the pledge (unless the pledge came first). In retrospect, it all seems designed to make a JW stand out.