The liquid soaking the dollar bill is a mix of alcohol and water. As the alcohol burns, the water evaporates. Why doesn't the heat from the burning alcohol cause the bill itself to char or burn

Because heat causes alcohol to volatilize, instead of burning it.

The combustion is not fulfilled since this is detached from the surface of the banknote that would be the necessary product to burn, in addition to considering that the necessary temperature is not reached

Explanation:

When water and alcohol are joined, they form a solution with high evaporation power, plus alcohol that has a higher degree of volatility than water, this is how these liquids are not retained on the surface of the banknote with heat and they are not it burns.