In Japanese Buddhism you do have this school which has a superficially sola Scriptura-like tenet.
Nichiren Buddhism was founded by the monk Nichiren, a 13th-century Japanese Buddhist monk who based his entire philosophy on a Buddhist scripture (dating from the 1st century BC-1st century AD) called the Lotus Sutra.
Now this sutra actually occupies an important place in a number of Mahayana Buddhist (the form of Buddhism that was transmitted to East Asia) schools, such as Chan/Zen and more prominently, in [Tiantai](“a 13th-century Japanese Buddhist monk”)/Tendai. (Nichiren was originally a Tendai monk.) Nichiren, however, was unique in that he claimed that only the Lotus Sutra held the key to true Buddhahood and is the only true scripture for this age; all the other sutras are either false or outdated.
In fact, he blamed all the other Buddhist schools pretty much for what he claims was their neglecting the Lotus Sutra for other scriptures; only faith in the Lotus Sutra could save people and the nation. (Nichiren was a nationalist, in the sense that he drew a link between the natural disasters and the civil unrest that was afflicting Japan at the time as a sign that the popular forms of Buddhism at the time were inefficacious. In his POV, ‘orthodox’ Buddhism (i.e. Buddhism as he interprets it) was the key not just to enlightenment of individuals, but also the security of the nation.) That’s why Nichiren Buddhism, rather uniquely among Buddhist schools, engages in active evangelization/proselytising (shakubuku ‘to break (and) subdue’) - because they believe that all the other forms of Buddhism had gotten it wrong all along.
Apparently, Nichiren took the following words of the sutra literally:
“Medicine King, now I say to you,
I have preached various sutras,
and among those sutras
the Lotus is the foremost!”
“[A]mong all the rivers, streams, and other bodies of water, for example, the ocean is foremost. And this Lotus Sutra is likewise, being the most profound and greatest of the sutras preached by the Thus Come Ones. Again just as among the Dirt Mountains, Black Mountains, Small Iron Encircling Mountains, Great Iron Encircling mountains, Ten Treasure Mountains and all the other mountains, Mount Sumeru is foremost, so this Lotus Sutra is likewise. Among all the sutras, it holds the highest place. And just as among all the stars and their like, the moon, a god’s son, is foremost, so this Lotus Sutra is likewise. For among all the thousands, ten thousands, millions of types a sutra teachings, it shines the brightest. And just as the sun, a god’s son, can banish all darkness, so too this sutra is capable of destroying the darkness of all that is not good …]”
Of course, this is not true sola Scriptura, because Nichiren never really made it necessary for the people to actually read the Lotus Sutra. He believed that the scripture was so efficacious that one did not even have to study or even read it: even simply believing in it and reciting the work’s title (Namu Myōhō Renge-kyō) was enough.