I have burned the bottom of my pot while making rice and chicken stew. How do I remove the burnt taste?

I assume your question is how to remove the burned left overs from the pot. Well, Try to soak it with boiled water for some time and then scratch it off.

I have found that adding a little vinegar to a pot of water and letting it come to aboil makes cleaning much easier.

Actually, my question is: How do I get the burnt taste out of my stew without having to dump out the whole pot and starting over (which I ended up doing)

Unfortunately there's nothing else to do...

If you notice on time you can remove the burned parts and serve the rest. Make sure you don't stir before you do this, or you'll increase the portions that you have to throw. If the charred taste infiltrated the entire dish, it's a goner.

Try to lower the heat, maybe find a way to spread the heat in a  more even way. 

As to the cleaning, surprisingly enough adding a large spoon of laundry detergent to the boiling pot and allowing to boil also works like a charm. 

one way to avoid this in the future is to slice a potato thin-ish and layer them around on the bottom. It makes a tasty snack too! (assuming you avoid the burn altogether) If you dont like potatoes you can always use pita bread. just put it in the bottom and it will take the heat for you, again you can enjoy it on the side if it doesnt burn!

Try coating your pot with olive oil first and if needed add a little more later to the stew; Olive oil has a higher tolerance to heating. You can also rub sprigs of chives into the metal; the oil in the chives are a treatment used on woks.

If there is a next time when your foods burning, when you are stirring if you notice A LOT OF STICKING to the bottom, dump what is not stuck into another pot or container; gently salvage what is stuck but not burnt and dump into the trash what is excessively brown/black. If you're food is burning you may be either trying to cook it too fast/too hot; or your pot is not conducting the heat well. I found that when I could afford them one at a time, buying the $60+ heavy pots improved my cooking, vs the $60 a set cookware.

Consider cooking stew 1 to 3 days before you want it. This gives the flavors a chance to meld. Also you can cook slowly because you won't be rushed to serve it that day.

so all i have to say is sad day....unfortunately i did the same thing and was reading all the answers to try and save it...well none of them helped i do suggest not doing all the suggestions to your stew....i was reading and someone suggested milk so i added it another person suggested peanut butter so i added it, that didnt work so i kept reading someone said some baking soda might help so i tried it well that didnt work so i kept reading....and finally someone suggested vinegar you see where this is going...i ended up with a volcanic stew that smelled like amonia haha all well i learned from this one

I can tell you what my nana used to do: turn the content of pot into meat balls (adding minced meat, onviously) and calling them "smoked" - the charred flavour taking first seat, naturally.