No, Nigel, the Mums as a group aren't Flat-Earthers. I used that absurd conspiracy theory to emphasize that the Moms For Liberty are anti-science.
That said, some people having the same agenda as the Moms are Flat-Earthers. Such as Kandiss Taylor, the chairwoman of the Republican Party in the state of Georgia, and a former candidate for governor. During one of her podcasts, she was skeptical of the idea that the Earth is round. "Everywhere I go, every store, you buy a globe, there’s globes everywhere—every movie, every TV show, news media, why? That’s what they do to brainwash. For me, if it is not a conspiracy, if it is, you know, ‘real,’ why are you pushing so hard?” https://newrepublic.com/post/172902/georgia-gop-chair-earth-really-round-many-globes-everywhere