He is still your fience. No evidence that he is really doing practically wrong there besides messing online. Not good but not bad enough that you start thinking of other way around.
This turf war kind of mentality is actually not helpul for women and unless he is totally out of contro,l use some cool behavior and be patient.
Men do things what pleasess them without really be so dedicated to the person who they are flirting. Some men just flirt. Let them.
As long as he is still committed to you and marrying you. Let it go.
You have to have more reasons to be worried about things like that. Just tell him you do not like that. But do not go to extreme.