We also have to take into account that Kennedy is still a teenager (according to the age range of the potentials), so she might seem to be a brat at times, but I think that it has a lot to do with her age as a character.
Kennedy is 19 which is the equivalent of Season 4 Buffy, Willow and Xander. Dawn is approximately 16 in Season 7 and shows far more maturity than Kennedy does. Also Kennedy acknowledges she's a brat, which is WORSE than if she was completely unaware of it, because it means she is aware of her bratty behaviour yet does absolutely nothing to try and change it.
She is the only one who wants to be a slayer.
That's debateable. Sure, she talks the talk but her actions say otherwise.
First off, she says she might be too old to be called as a slayer. Secondly she skives off going to the desert with the other potentials. Giles isn't taking them there for a holiday, it's clearly a part of the training, yet Kennedy seems to think it's beneath her. Thirdly, during the training session in the backyard, Kennedy isn't joining in (as in she performs the moves as she shouts them out to the others). Instead, she's barking orders at them then publicly humiliates Chloe and GLOATS about it just because Chloe confused her left and right which is such an easy mistake to make. Also Buffy was teaching "Do what works for you and you might just survive", Kennedy was teaching "Do as I say or else". Fourthly, all Kennedy cares about is having a bigger say and lording it over others, she openly admits to Faith that she thought she'd get a bigger say with Faith in charge unlike with Buffy (hence the brown nosing of Faith beforehand), also immediately after Buffy is kicked out of her own home, Kennedy is the one saying "I think those of us who have been here the longest should get a bigger say"- Considering the two potentials Kennedy arrived with are dead, that makes her the one who has been there the longest ergo she's already trying to seize power. Lastly, Kennedy avoids a hell of a lot of the last fight and only turns up right at the end before Spike sacrifices himself. Surely it would've made more sense to have Xander with Willow (since he talked her down from Dark Willow last time and as he said in Grave, "World gonna end, where else would I want to be?" other than with his lifelong best friend) and have Kennedy on defence since she is supposedly trained to fight and "wants to be a slayer".
She allows herself to be used as bait to catch one of the Bringers.
As the oldest and "most experienced" potential (since she clearly feels she doesn't need to go to the desert with the other potentials), it makes sense to use her rather than one of the younger ones. It's about time she started pulling her weight instead of just throwing it around the place..
She intervenes on Willow's behalf to actually solve the problem of attachment to someone who is dead.
It wasn't Kennedy's place to do so. Kennedy was only thinking about Kennedy, not about Willow. Tara has been dead for less than a year, Willow is still grieving, yet Kennedy does not give a damn. All she cares about is raising her position within the group and Willow is the means to do that, hence why as soon as she's officially "dating" Willow she starts showing up at scooby meetings, trying to insert her opinions and demanding that Willow sides with her over Buffy. All the other scoobies (Tara, Spike, Anya, Oz) weren't involved in Scooby meetings right away, they had to earn their place, Kennedy just expects one to be handed to her.
Also, it's up to Willow to decide when she's ready to move on, not have her hand forced by Kennedy. Willow is begging for forgiveness from Tara, that doesn't scream "ready to move on". Kennedy caused the problem in the first place yet somehow doing exactly the same thing solves the issue and "cures" Willow of her grief. It doesn't work like that.
She shows some leadership characteristics.
She has an inflated ego and bosses people about. There's a difference.
When Willow kept transforming back and forth between Willow and Warren, Kennedy did not run off screaming like most people would have, she stayed to ensure the problem would be solved.
As
@punchkicker15 says, Buffy and Xander had to take a level in idiocy all so Kennedy could save the day. It's bad writing. The Killow relationship was so forced, even if (and it's a big if), Willow had decided of her own free will to move on from Tara, a new relationship would not have reached the level of importance or significance that the writers tried to make out Killow had.
Full marks to Kennedy for helping Willow avoid becoming the tragedy we lived next to for ten years.
You're being very judgemental of your former neighbour, especially as you said she remained single ""by choice". You might not agree with her choice, and that's your prerogative, but it's not up to you to decide whether or not she should've moved on. Everybody is different, there is no time limit on how long it takes someone to grieve.
It was clear that Willow wasn't ready to move on yet, but Kennedy forced her to because it suited Kennedy to be dating her so she could have access to the scooby meetings. Kennedy then expects Willow to side with her over Buffy, despite Willow and Buffy being best friends for 7 years. "Forcing" someone to do something takes away their agency.