Haven’t dealt with this specifically, but I’ve worked in coffee shops for over a decade so I’m familiar with this phenomenon. When you heat milk above ~100°F, the proteins and fats denature and solidify on surfaces, creating the brown “crust” and funny smell you’re finding in your kettle.

If I were you, I’d try using Rinza, a product which coffee shops use to clean espresso machine steam wands and milk pitchers. Rinza ain’t cheap, so consider if your kettle is worth the purchase.

If you do decide to buy Rinza, try this:

1. dilute Rinza to the recommend strength on the bottle with room-temp water
2. fill the kettle to the “max” line
3. let that sucker sit for a while to soften the “crust”
4. turn your kettle on to boil (it may smell terrible)
5. let it boil for a couple minutes if your kettle will allow. The heat and chemicals and gentle agitation from the boil should be pretty effective in loosening the crud inside
6. pour out the liquid, try gently cleaning whatever is left over with a soapy sponge, assess and potentially repeat the process
7. once the milk scum is gone, boil and discard 2-3 more kettles’ worth of water to rinse away any residual chemicals

Tbh, Rinza is expensive but worth it for this particular problem. If you’re a regular at a cafe, you may be able to ask the baristas there for a small amount of their cleaning supplies. Tip well if you go this route!

Best of luck!