Overall, it's just assumptions. Btw, I am pretty sure that Minato said that Kushina taught him Shiki Fuuin, because a jinchuriki couldn't use it.
Who taught it to Kushina? Mito, possibly. Anyway, the symbolism with the fire to Minato is also just a bold assumption. Kishi often uses the same drawings/symbols over and over, and often proves to have no important relationship. It helps to make us theorize, but I doubt it has a deeper meaning.
Also suggesting this helps the theory of Ridukou being Uzumaki. Well it is the most obvious answer, but just recently, I would believe that Kishi put further doubt on this. The man, who knew absolutely most about SO6P, namely Uchiha Madara, said to Zetsu/Obito that Nagato was of the Senju lineage. In other words, Uzumaki originates from the Senju clan.
Of course, after reading Naruto for quite a long time, you would start understanding, how Kishi writes etc.. So it's possible he just said that to put his readers off road, regarding this subject. Shortly, manga evidence goes against SO6P being Uzumaki, which is why, Kishi will make it that way. To "blow" our minds. Just like with Obito, the 4 kages, etc..