One possible fanfiction idea could be that Kim and Adam have a baby unexpectedly. They initially struggle with the new responsibilities but then grow closer as they face the challenges together. Maybe they have to deal with work - life balance while also protecting their new family from the dangers of their job.
Another theme is the challenges they face together. This could be anything from dealing with a difficult case to facing problems within the department. In these fanfictions, their relationship is tested, and we see how they overcome these obstacles as a team and as a couple.
In this fanfiction, the baby might be a key to bringing some long - lost family members of either Kim or Adam back into their lives. The couple then has to deal with the new relationships while also taking care of their baby. They might also face some judgment from others about their relationship and how they are raising the baby, but they stay strong together and prove everyone wrong.
One great fanfiction could be 'Unexpected Moments'. It beautifully captures the chemistry between Jay and Kim leading up to their kiss. The author does a wonderful job of building the tension and making the kiss seem very natural within the story's context.
You can start by looking on fanfiction.net. It has a large collection of fanfictions for various shows and characters, and there's a good chance you'll find some great Jay Halstead and Kim Burgess kiss fanfictions there.
I've found that Tumblr also has some amazing Jay Halstead and Kim Burgess fanfiction. You can search using their names and relevant tags. There's a story I remember where they go on an undercover mission together and it really tests their relationship. It was full of action and at the same time, you could see the underlying connection between them. It's a great read if you can find it again.
Some Burgess characters could be a bit skeptical of the Guardians at first. They might think the Guardians are just stories. But when they actually meet them, they start to have a more hands - on interaction. Like a girl from Burgess who challenges Toothiana to prove she's real by showing her where all the teeth are hidden in Burgess. This leads to a fun and adventurous interaction between them.
Complex themes. For example, in 'A Clockwork Orange', there are themes of good and evil, and the power of conditioning. Vivid characters are also a feature. In 'Earthly Powers', the characters are well - developed and their relationships are intricate.