No, no no and no.
Here is why:
Poison - These poisons are made to kill ants in your house. These are worker and scout ants. If you pour it onto the hive, the ants will either not eat it after the first few died, or avoid the area where the other ants died. In any case, you will not be able to kill the queen(s), who keep producing the ants.
Fire - The three-feet anthill can be aproximated to go as deep into the earth. The queen is usally deep below, the fire will not reach her, since deep down there is not enough ari for combustion.
Here is the only work to get rid of an anthill permanently:
Buy a pair of fishing pants of better yet a full body suit, as used for painting rooms. And a shovel. Then dig up the anthill and toss the earth into bags. If you are lucky you will see the queen's chamber, that is when you know you can stop digging. If you don't see it, you will have to keep digging until there are no more ants.
And here is how I know all this stuff:
I spent almost all my childhood in an extensive warfare with an ant-colony in my parten's garden. I won by unleashing the nuclear fury of shovel and bag. The place where that anthill used to be is still a slight pit.