Dealing with the Bakumatsu era, or the final years of the Shogunate, BKI is an interesting, if unsatisfying anime - based largely on actual historical events such as the secession of the Republic of Ezo and including fictionalisations of its leaders. Well animated and researched, the show looks well, and gets the look of the period right, evoking the wider political conflict by presenting the incursion of Western fashions into Japan during the period.
However, the show largely missteps by introducing supernatural and magic elements to its plot. Not only are the supernatural elements of the plot ill-explained and confusing during the early episodes, but they remove agency from the characters, and reduce what could be conflicted, complex characters to stock good versus evil stereotypes. Compared to a show like Rurouni Kenshin, set a few years later, BKI's characters lack the inner conflict and acknowledgement that by taking sides either for or against the nascent Meiji government, they are cutting themselves off from old comrades. The magic adds nothing, and seems merely to exist to provide over the top set-pieces.
The best elements of BKI come in the moments between the supernatural - the political organisation of the Ezo Republic, the interesting use of the travelling actors, among the best characters, to frame the story. Our lead character, the wandering swordsman, feels too generic, however, to really entertain, and is more an amalgamation of generic wandering samurai tropes than a really interesting character in his own right.
BKI has some interesting ideas, but it undersells itself, and amps up the action and the magic when it could be something really special and give us an insight into the political situation of the late Shogunate. For fans of samurai tales, there's a lot better out there, but it's worth a look-in, if only for the animation and travelling actors.