If you don't like the smell of vinegar: A 5kg bucket of food-grade citric acid powder costs 20€ and will last you a lifetime. I literally bought mine when I was an apprentice over 20 years ago in my first one room apartment. It has moved nine times with me, it is half empty by now so when predictions are correct, I'll have to get another one for retirement.
Fill the kettle, add a teaspoon of citric acid, boil for a second and let it sit. You'll see small bubbles rising where the limestone deposits are being dissolved. That fizzing is carbon dioxide escaping: limescale is mostly calcium carbonate (CaCO₃), and the citric acid attacks it, breaking the carbonate apart. The calcium gets bound up by the citrate into calcium citrate, which washes away, while the carbonate leaves as CO₂ (the bubbles) and water.
Roughly, the reaction looks like this:
3 CaCO₃ + 2 C₆H₈O₇ → Ca₃(C₆H₅O₇)₂ + 3 CO₂↑ + 3 H₂O
Citric acid is a weak acid, so it happily eats through chalky scale but simply doesn't react with stainless steel, glass, or plastic, whatever the dose. The one teaspoon rule isn't about protecting the kettle, it's just about not wasting powder and not having to rinse forever. Use more and it works faster and fizzes harder.
The one exception is bare aluminium: citric acid can dull or lightly etch it, so don't use this on an old aluminium kettle or pot.
Once the bubbling stops, the reaction is done: everything that could dissolve has dissolved. Pour it out, give it a quick rinse or the next coffee will have a sour note, and the kettle's clean, no vinegar smell.
EDIT, because I only now read OPs post properly: I've only used this on electric kettles - I wouldn't even know any other ones, I mean, unless you count the ones you put on a burner at a festival or something like that. Those never saw enough sustained use to build up limestone for me.