Ἤκουσα Ἀρχεδήμου ὅτι σὺ ἡγῇ χρῆναι περὶ σοῦ μὴ μόνον ἐμὲ ἡσυχίαν ἄγειν, ἀλλὰ καὶ τοὺς ἐμοὺς ἐπιτηδείους τοῦ φλαῦρόν τι ποιεῖν ἢ λέγειν περὶ σέ
the meaning is something like this: I have heard from Archedemos that you reckon that not only I should keep silent regarding you but my companions also should [refrain] from doing or saying anything bad in your respect.
is this τοῦ a Gen of infinitive of purpose?
No, that would give the opposite meaning, but your “refrain from” is right. The genitive will depend on ἡσυχίαν ἄγειν, cf. Pl.Rep.583e ἡ τῆς ἡδονῆς ἡσυχία λυπηρὸν ἔσται (a separative gen.). It would be better without the comma, despite the ungainliness of having περὶ σοῦ and then περὶ σέ (or περί σε enclitic?).