Passing “main_color” to the color attribute will make your icon inherit the Theme Main color:

[icon icon="heart" color="main_color" size="small" icon_solid="yes"][/icon]

If you further want a brand new color different than you main theme color, you can create a class for it, then pass that class to the color attribute. Here’s an example:
Say you want purple, add these to your stylesheet.css (or Custom CSS in Theme Options):

.shortcode_icon_solid.shortcode_icon.purple {
	background: purple;
}
.shortcode_icon_simple.shortcode_icon.purple i{
	color: purple;
}

Then go ahead and create your icon:

[icon icon="heart" color="purple" size="small" icon_solid="yes"][/icon]

Greetings!