ha-gever ve-ha-ishah okhlim pastah ba-meesadah ve-leakhár meekén (akhar cakh) hem shotim kafeh
Is לאחר מכן some sort of fixed expression?
Yes, and it means "afterwards".
The word כן used to mean something like "so" or "like that". However in modern Hebrew this meaning of כן is used mainly in fixed expressions, like "אלא אם כן" (=unless) or "על כן" (=therefore).