Can you extend shelf life by reheating? I marinated a couple of chicken breasts overnight in the fridge

The next day I baked it (in the same ovensafe dish it was marinated in) until fully cooked through

After baking, the chicken is still fully submerged in the marinade

I let it chill 30 min at room temp and then put back in the fridge

StillTasty says it will last 3-4 days refrigerated

If on day 3 I reheat, rebake or even boil it for 10 minutes, will it kill all bacteria that were present and multiplying during those 3 days in the fridge? In other words, can I restart the 3-4 days count whenever I recook the chicken, so that it will last indefinitely?
What you're concerned with when it come to food spoilage is the toxins bacteria produce, not the bacteria. While heating it will kill the bacteria, the toxins are typically proteins which will not be destroyed until your food has been turned to charcoal. Heating it will thus not increase the shelf life. On the contrary: heating and the cooling means your food has been in the 'danger zone' for longer than if it was refrigerated the whole time.

If you want to increase the shelf life of a dish like you described, freeze it. If frozen as soon as it comes out of the oven, it will last for several months in a normal freezer. The sooner you get it frozen the better for extending shelf life.