So is this co-worker actually trying to steal him, or is she just being friendly and your boyfriend is eating up the attention? Because there’s a difference. A woman can’t steal a man who doesn’t want to be stolen. He’s making choices here too.
If she’s explicitly flirting with him and he’s flirting back, that’s on both of them. But it’s especially on him because he’s your boyfriend and he should be shutting that down immediately. If he’s not, then he’s enjoying the attention and that should tell you something about where his head is at.
Talk to your boyfriend about it. Not in a crazy accusatory way, but say “I’ve noticed your co-worker crossing boundaries and I need to know how you feel about it.” His reaction will tell you everything. If he gets defensive or tells you you’re being crazy, that’s a red flag. If he takes it seriously and makes changes, maybe there’s hope.
And honestly, if he works with this person every day, is this drama something you want to deal with long term? Because she’s not going anywhere and neither is he. You might be signing up for years of checking his phone, wondering what happened at the office Christmas party, and driving yourself crazy. Life’s too short for that.