Have i used the word 'insignia' correctly?
No. According to my dictionary, insignia means a mark or badge that indicates rank or membership in an organization. It looks like you're trying to use it in a metaphorical sense -- espousal is an action, it cannot literally be a physical object like a badge. The metaphor fails because the comparison between progressive thinking and the kind of organization that would indicate membership with an insignia is weak.
There are better word choices to get your point across. You could say that "espousal of modern learning mediums" is a hallmark or a sign or an indication of progressive thinking, for example. The word badge is sometimes used metaphorically, so you could say that "espousal of modern learning mediums" is a badge of the progressive movement.