His response to your asking him about it got cut off here. I don't think you're wrong to have "alarm bells" sounding, but I'm not sure you should jump to conclusions right now either. I'd think someone old enough to be married for 20 years would be too mature for "text flirting", but I suppose some people "join in" with what younger people do.
On a separate thing, it's kind of too bad he knows you were going through his phone; because that could potentially make you seem to "nosing around" in his personal business - never something people like. Then again, if he leaves the phone around and makes no effort to keep it to himself, maybe he doesn't feel he has anything to hide.
Maybe it depends on whether he's always been an "overall flirt", and you just haven't seen him because he behaves when you're around; or whether he's generally a "non-flirt" kind of guy (they do exist) and is doing something way out of his usual character?
I don't think you're wrong not to be "too thrilled" about it, though. Sometimes when someone knows s/he is guilty of something s/he tries to make the other person feel wrong. You're not wrong. Smily faces and "hi" are one thing. "Can we be friends" and Valentine messages are another. I don't know what I'd do in that situation - just wait and see what unfolds (maybe through calm, reasonable, conversation).