boyf and Instagram

So today my boyfriend went on my phone and look at my Instagram. Looked at my search history (which was nothing because I don't really search anyone up) and then I said well since you're not trusting me, show me yours. Which I only said since he was doing it to me, I didn't actually care. But he was like nah we need to trust each other and aparently 'joking around' hides his phone from me and doesn't let me look at it. 
He's saying I'm being stupid and he was just joking around but he wasn't, I saw him trying to work out how to delete it and he took his phone with him. 
Am I being stupid for feeling uncomfortable and suspicious? 
Not saying I don't have trust in him but why would he be like this?
He has flirted with other girls while we have been together which makes me feel more insecure and uncomfortable