How much calories should you burn per day to reduce 1 kg per week?

No way to tell, as it depends on how many you are eating, and how active you are.

Let's say you're already on a strict diet of maybe 1200 cals, then you shouldn't need to burn any more through exercise to lose 1 kg/week

Or maybe you've pigged out on a 4000 calorie double cheese Pizza, then you'd need to burn 2500-2800 cals to loes weight. and that's assuming that pizza was the only thing you ate that day.