He is having a moment of remembering their short encounter as a child. In a field of flower, Rozentine with her innocent face while holding flowers. He knew all along who is she and always adore her dearly. I hope further chapter will be their moment spending time with each other.
Yeah, he was indeed use your handkerchief because it is expensive and the fabric is soft. He's not flirting on you at all (=・ω・=)