Your question vaguely suggests you're looking for permission to do something that already doesn't sit well with you. That says quite a bit right there.
Still, here are two tests to help you determine whether or not your behavior is appropriate: 1) If your current bf read these texts, would he be infuriated and/or possibly dump you? 2) If you found out that your current bf was having a similar conversation with an ex (or fwb) and assured you nothing was happening in real time, would you believe him and/or trust him after that? Even if it were true, since you could not independently verify his claim, would it not eat at you?