I think in this case the verb 'fly' is part of the expression 'will never fly'. It's a figurative way to say that someone or something will not succeed. Considering that 'talk smack' means to criticize someone/something, the individuals disrespecting and 'talking smack' about the person behind his back may try to convince the speaker that said person deserves the criticism and lack of respect he gets from them. However, they'll not succeed as the speaker doesn't seem to care and will likely remain on good terms with the person in your sentence, regardless of what anyone says about the latter.

It means that they will not succeed, that what they say will not be accepted. ‘It will never fly’ is an idiomatic expression. Idioms can be confusing at first, but they are super cool when used in the right context. I hope this helps ☺️