Tony Stark is a flirt (see Christine Everhart and Pepper herself in Iron Man, Natasha Romanoff in Iron Man 2, Maya Hansen in Iron Man 3), like his father before him (see Peggy Carter in Captain America, and various women in Agent Carter). Flirting is not generally an indication that you’re looking to start a relationship and become someone’s surrogate dad; with Tony, it’s definitely not.
In Spider-Man: Homecoming, he makes one reference that I can remember to Aunt May’s attractiveness (in the ‘alibi video’ he makes with Peter), and immediately corrects himself as behaving inappropriately. Given his general level of flirtiness, this doesn’t seem contradictory to the later revelation that he and Pepper have worked things out post-Civil War.
The ‘thread’ isn’t May/Tony; it’s “Aunt May is attractive”, and was likely a reference to the fan reaction at Marisa Tomei’s casting.