The implication is that their relationship status is pretty well established. They appear to be in a committed monogamous relationship, albeit one they keep almost totally hidden from the rest of the crew and us, the audience. There's also a certain element of not really wanting to admit to each other how close they've gotten. Hera also uses her close relationship with Kanan to manipulate him (emotionally) into doing things her way, especially when she calls him "love".
This dialogue from "A New Dawn" (before the start of Rebels) strongly implies that while Hera is open to flirtation, she's really not interested in maintaining a serious relationship.
He obviously liked her starship, she could see as he walked around it.
That was good. He was also smitten with her, she could tell—and she
was all right with that, too. She didn’t want to tell him that her war
had already begun, and that in war, there was no time for anything
else. He would probably understand that eventually.
With that in mind, in the short "The Machine in the Ghost", they're clearly about to kiss when interrupted by Chopper. After a brief bit of banter, they give him a bunch of chores to do elsewhere on the ship, the metaphorical equivalent of giving him $10 to bugger off to the cinema.
And in the Star Wars: Rebels - Rise of the Rebels novel, we have the following internal voice from Hera's perspective:
There was nothing but static. If the TIE’s blasts had somehow hit the
turret and she’d lost Kanan, she didn’t know what she’d do. Kanan
Jarrus was more than a friend or a colleague. The human meant the
world to her—although she’d never admit it to him.
and this quote from Hera's character actor Vanessa Marshall shows that the relationship is a lot deeper than even she's been told!
So I don’t see much schmaltzy romance, on the page. When I watch the
episodes and I’ve seen some gestures and body language that wasn’t
described in the script, as far as I recall, I thought, “woah, wait a
minute!” I remember being at Star Wars Weekends and they played that
initial short where the two of them are bickering and Chopper is going
between them. At the end, they sort of come together, and I remember
sitting there watching it, going “hey now! What was that?” Everyone
was asking me, and I had no idea! I didn’t get a sense of that while
reading it or recording it! So it’s interesting to me to allow what
may happen in the animation, a caress or a look, that indicates a
And of course, the final season makes it abundantly clear. They kiss, she tells him that she's in love with him and they ultimately have a child together