How many calories do you have to burn to lose 1 kilogram of weight/fat?

Weight is a measure of mass relative to the center of the earth. 

Fat you are referring to is a fantastic tissue that holds lots of energy stored as glycogen.   When fat cells get full and run out, new ones are created in a process known as neolipigenesis. 

There doesn't seem to be a cap on neolipigenesis,  which makes it quite fascinating..

Not even related.   Fat is relatively light. 

If you're talking about burning calories through exercise, you're not going to lose much if any weight.  Weight loss is mostly about what we are eating.  Exercise is great for toning and keeping us strong. 

They say it takes about 3,500 unused calories for a person to lose a pound.  But i have no idea if this is true to science.  Meanwhile if you burned 3,500 calories exercising, the minute you ate something again, many of those calories would return to your body.

If you want to lose weight, use the Ketogenic diet.  It works

When you first start off the calories in a lb or kg of fat is less than when you have a small amount of body fat. It goes from 2400 roughly to 3500 calories. That's why people plateau or have a rough time losing the last 5 lbs.

7700 is about right. To put that in perspective, an average sized man would burn about 140 calories in running 1 mile- 1.6 kilometers. So you'd need to run 55 miles to burn off 1 kilogram. 

In theory you need to burn 3500 MORE calories than you consume, to lose 1 lb of fat. 1 Kilogram = 2.2 lbs so the calorie deficit would need to be around 7700.