A considerable amount of it between Winn and Superman, with the former turning into a Squeeing fanboy when he gets to meet him.
Also between Winn and Mon'El as they both go out for drinks and become instant buddies.
Also also, Winn and James (seeing a pattern here), especially in season 2 when James becomes Guardian and they spend their nights together fighting crime.
Kara once admitted that even she wanted to date Lucy Lane after she got to know her as Jimmy's ex-girlfriend for the first time.
Kara and Alex may be adopted sisters but they are rather close for that.
Cat Grant appears to be playing the role of Lois Lane to Supergirl's Superman. She's dismissive towards Kara Danvers and caustic about Supergirl, but has been shown to have a soft spot for both including several Hypocritical Heartwarming moments. Her interview with Supergirl mirrors Lois Lane's interview with Superman in the first film, minus the romantic flying scene. She is also the first person to figure out Supergirl's Secret Identity on her own much like Lois Lane in Superman II.
Kara and Lena Luthor quickly pick up a very Superman/Lois vibe once Kara becomes a reporter and uses Lena as her primary source. It also helps that Lena instructed her secretary that Kara is permitted to drop by LuthorCorp whenever she wants.
Later there is Lena asking Kara to come to her party and it looks like she is asking her on a date. Lena also tells Kara she's Lena's "only friend" and later shows up at Kara's apartment uninvited.
In "Luthors," Lena and Kara's friendship is put to the test. Kara is the only one who wants to find the good in Lena, even when evidence implicates the latter of conspiring with her mother. Lena is obviously touched when Supergirl tells her how Kara believes in her innocence. Towards the end of the episode, Lena is vindicated and she says to Kara "I've never had friends like you before... I've never had family like you before."
In "Exodus", Lena is pushed off her balcony and Kara rescues her, flying up while carrying Lena bridal-style. It's reminiscent of the way her cousin carried Lois Lane.
In "Ace Reporter" Kara hears that Lena is at dinner with her ex-boyfriend and runs off to crash it, which Mon-El even points out makes her seem like a Stalker with a Crush. They end the episode with a tender embrace after the ex's death, with Kara promising that Lena will always have her. Lena, meanwhile, flatteringly describes Kara as "the best reporter in National City."
In "Resist", Kara is very distraught that Mon-El and Lena are trapped on the Daxamite ship which the president has ordered destroyed.
Kara: But all I think about is the fact that two people I love are trapped on that ship and if we destroy it, then they're destroyed, too, and that will break my heart.
The entire last third of Season 3 can easily come off as a messy love triangle between Kara, Lena, and Sam. In particular, Supergirl trying desperately to repair her relationship with Lena after a breach of trust, and Lena having none of it, point-blank telling Supergirl that they aren't friends and don't need to be friends, because Lena has friends of her own. Supergirl (and Kara, one of those friends Lena was talking about) is very hurt by this.
Kara's confession scene in the season five premiere can come off as a love confession. Moreover, it is worth noting that Kara, arguably, never got this emotional with Jimmy or Mon-El. Furthermore, when she faced the prospect of dying while fighting Reign, Kara did not express any fear. However, when confessing her secret to Lena she voices the fact that the possibility of losing Lena frightens her.
Moreover, when Kara gifts Lena a signal watch at the end of the premiere, one could interpret the scene as a proposal of sorts because the Girl of Steel is reifying her trust in Lena via the gift.
Imra seems very starstruck and infatuated by Kara.