You'd have to write CSS to specifically style it. The below should work.
Code:
.masthead h3 > a {
color: red;
}
Add whatever styling you'd like then add it to the template.css file for flexistrap, which can be found below.
/templates/flexistrap/css/template.css
Any suggestions on how to do this? Or would I be better off building a logo with a transparent background to shove in there?
If you've no experience with CSS then yes that'd be a simple solution.