How or what is the best cleaner for a stained coffee pot?

Vinegar and water should do the trick. Brew it and then rinse...brew again (twice) with just water to get rid of the vinegar.

Run white vinegar through the brew cycle. and let it soak (maybe overnight.) Then run again with just water to rinse.

There used to be a coffee pot cleaner that works the same.

I have used dishwasher detergent on my thermos and it came out sparkling clean. A teaspoon of it in with hot water soaked overnight.

Try a few soft paper towels dampened with warm water and Dawn dish soap with a teaspoon of baking soda. This will work great on stains inside and out, all without scratching either surface. Rinse clean and enjoy a cup.

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I also use Dawn & baking soda on the bottom of my pots and pans. Cleans beautifully.