Assuming he says it in the most impersonal way, i.e. with a formal "to have intercourse" in infinitive, in Czech it would be:
Souložit mého hnědého psa!
A more slangy and natural way would be:
Jebat mýho hnědýho čokla!
And of course one can substitute "jebat" (to fuck) with prcat, mrdat, šukat, šoustat, píchat, vošukat, vymrdat, vopíchat, vojet, you name it. The advantage of using šukat is that in Polish, the homonym "szukat" means to search so it's not even that rude! Not to mention that archaically, šukat means "to tidy" so it's even less rude!