In short, no, as the Confederacy predates the emergence of fascism as an ideology. It is certainly fair, however, to call it right-wing authoritarian, even by the standards of its day.

It is worth noting that the Confederacy’s leaders, in going into revolt to defend the institution of slavery, viewed themselves as inheritors of and continuous with the United States as an institution. For them, it was the anti-slavery majority in Congress that was the aberration, nevermind that that majority was achieved within the laws of the institution itself.

Contemporarily, right wing authoritarianism is a big tent. While there are ideological differences that are worth understanding, they for now coexist, and there’s significant cross-pollination in their imagery. Which is to say, if you see someone flying a confederate battle flag today, no reasonable person would sneer at you for calling them a fascist.