I have a character for whom three of their most prominent traits are meant to be their kindness/high degree of empathy, social awkwardness/obliviousness to social cues, and overall introversion. I am trying to show, not tell, that they are supposed to be kind, but I am running into difficulty doing that because of the other two personality traits. Most of the time, I have noticed that authors who wish for their characters to be interpreted as kind do this through displaying a character's behavior in social interactions, either through extroverted individuals being publicly nice and supportive of others or for more introverted individuals being supportive privately when no one is looking (i.e., showing them being nice to/protective of strangers).
That doesn't really work for this character. They are rather anti-social, shy, and don't like to be around large groups of unfamiliar people, and while they do like to spend time with people they care about they often prefer to go off on their own than try to socialize. Therefore, they have fewer opportunities to display kindness/empathy or are less likely to be present when a situation does arise that would demonstrate this trait (i.e., assisting someone who needs help). Additionally, because of their social awkwardness and general obliviousness to social cues they might not notice if something is wrong or someone needs help even if they would care if they did notice, or have enough confidence to act.
The character does display kindness to the people they are close to, demonstrating through their actions that they care about the well-being of their friends and family, show concern over the emotional state of others, and in some cases come off as desperate to please them. However, I've noticed this doesn't seem to make them come off as notably kind compared to anyone else, especially when in public their demeanor often comes across as icy and when their buttons are pressed they can be nasty and brutal (which is intended to be a character flaw), which seem to "cancel out" any otherwise empathetic behavior. They come across as "mostly nasty with a kind side" rather than "mostly kind with an occasional nasty side they don't like to acknowledge". The issue is that while "kind", "shy", and "socially awkward/oblivious" aren't contradictory personality traits, they latter two can easily mask the first in a way that makes it hard for the reader to pick up on.
The only other way I have noticed authors display a character's kindness is to show the character is kind to animals. While it fits with this character's personality, it also feels like a rather brazenly unsubtle attempt at gaining audience sympathy.