I think a lot of people are mistaking the change in Gio's body language to be him "looking adoringly" at Rose, when it is actually just him being more conscious of directly facing her when speaking and making accommodations for her deafness.
This is epecially noticeable in the studio when normally the couples will look at the Judges/Tess and Claudia/Rylan or Janette when speaking, with just the odd glance towards their partner if/when they are talking about them or it is a collaborative question. Gio, on the other hand, faces Rose, or at least positions his body more towards her, and looks more at her than at the other person, to allow her to lip read easier.
I have also noticed that Gio is more tactile, but again it could be because he is being flirty or just because, with Rose being deaf, he is adapting to using physical cues to get her attention - rather than calling her name, he touches her arm; where other couples can use vocal cues for remembering steps/shapes, Gio physically moves Rose's body (eg a hand on the small of her back when she needs to arch her back more vs Aljaz calling out "banana" to remind Sara to arch more) etc.
All of these things can be interpreted as "flirty" and "adoring", especially considering Gio's reputation, but I genuinely think it is just him trying to adapt to being partnered with someone with a disability and making the necessary accommodations for it.