He is not treating you very well.

You could tell him that you want to improve your relationship with him by asking for what you want. You could tell him that you would like a romantic caring monogamous relationship. Ask him what he wants, with you.

You might end up being the one to change the relationship, you even might leave him. If you decide to do so, to be the one to make the first active change - you could take this as a sign of your strength and belief in yourself. You deserve a good relationship.

Right now it sounds like he is trying to get the "best" of both worlds. That is not fair to you unless it is something you both actually agreed upon.

If you two have an agreement to be faithful, but he is flirting and stepping outside the relationship, then it is important for you to be safe. He's hiding things from you and eventually that could mean that he has an affair. Which could put you at risk.

You ask how to trust him. I personally believe that a person needs to be trustworthy first before we trust them.