Does texting flirting count as cheating?

After I told my boyfriend I was "so done" after a big fight one night, he reached out to a female classmate of his. She has a young kid and may or may not still be with the child's father. I found the texts when I was using his phone to look up directions, and another text came through, then her name caught my eye since I didn't know her. Then yes, I did scroll through their convo. (Please spare me the whole "snooping" lecture.)

In the texts he thanked her for sharing her sandwich with him earlier that day and that it made him feel loved. Then he asked what she was doing, and she said just putting her kid to bed and cleaning up, saying something about being an "old soul". Then he said he's an old soul too, and she said yeah it's kind of bad at her age, and he said something like "nah we're perfect." Then he said he wished she lived closer so they could grab drinks. Then that was pretty much it.

When I called him on it, he said that I had said I was "done" with him, and that she's just a friend from school, and he wanted to someone to vent to about us, especially since he had already asked her for advice in the past. I really don't know what to make of the situation and don't know if I'm blowing it up more than it actually is. Please help.
Does texting flirting count as cheating?
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