Can you color a flame and what would the effects be?
Unfortunately not, I'm afraid.

I think you might have gotten cause and effect mixed up here. Blue flames are hotter than yellow flames not because of their color, but because hotter flames generate blue light and cooler ones generate yellow/red light.

To take an example of this kind of problem, I know that very red tomatoes tend to be tastier than very pale tomatoes. Does this mean that we could make tastier tomatoes by injecting food coloring into them? Well, probably not, because it's not the color that causes the flavor. Rather, tomatoes that generate more color tend to also generate more things like sugar and flavors, and so flavorful tomatoes tend to have more color.

With flames, it's even more black-and-white because while its possible to have a pale tomato that happens to taste good, the color of the flame is set by the universe: unless you add colors yourself, it is impossible to have a blue flame that is the same color as a yellow one. The color of the flame is determined by something called "blackbody radiation," and if you're curious about why flames are colored the way they are, it's definitely something to take a look at.