You are exactly correct. The water in the pot will boil at 100C and continue to do so until it is ALL gone. AFTER that what remains in the pot (air) can get above 100C. As long as there is water in the pot, ALL of the heat energy applied from the stove burner (except what escapes into the surroundings) goes into converting water liquid into water vapour which floats away into the room, and there is NO temperature increase above 100C.
As a result of this, the material inside the flask experiences a constant surrounding temperature of exactly 100C as the water boils. Thus it can NEVER exceed that temperature, because heat can flow into it only from a HIGHER temperature source.
This is exactly the principle in using a double boiler pot for cooking - the item you are cooking in the upper pot never gets hotter than 100C, which prevents its sensitive ingredients from burning. The same concept is used in sous vide cooking - place the food in a bag, remove the air and seal, then immerse in boiling water. The items will cook slowly at exactly 100C as long as the water boils.
Decades ago I forgot all this and tried to make fudge in a double boiler. To do that you MUST raise the temperature of the sugar/milk/etc. mix well above 100C to convert the ingredients to the proper mix of fudge components, and you use a candy thermometer to monitor the temperature and judge when to quit cooking. When you do this in a regular pot directly on the burner, the fudge mix loses water and changes its chemical composition substantially as it boils, raising its Boiling Point temperature.But in my double-boiler event, the fudge-to-be mix never went over 100C! THEN I remembered why!
This also links to a common error in cooking by boiling. When doing that (say, boiling a pot of potatoes), many people will keep the burner up at highest setting to make the potatoes cook faster. BUT inside the pot, the potatoes only experience a temperature of 100C at all times as long as there is water boiling in the pot, no matter what the stove burner setting is. A high burner setting merely means that the water will boil away faster and there will be a higher rate of steam leaking out from the lid. This does NOT speed up cooking the potatoes. You only need the burner setting to be high enough to keep the water just boiling.