One common theme is their relationship. Writers often explore how they support each other through the traumas they've experienced in the Hunger Games world. For example, Finnick's protection of Annie.
Fanfiction.net is also a great place to look. A lot of Hunger Games fanfic writers post their works there. Just be aware that the quality can vary a great deal. You might need to sift through some stories to find the really good ones about Annie and Finnick.
One common theme is his trauma. Given his experiences in the Hunger Games and his exploitation, many fanfics explore how he copes with that. Another theme is love. Finnick's relationships, whether it's his love for Annie or his friendships, are often central in fanfics. And there's also the theme of resistance. As a strong character, he is often depicted as part of the resistance against the Capitol in fanfics.
One common theme is trauma recovery. Given Annie's experiences in the Hunger Games, many fanfics explore how she deals with the mental and emotional scars. For example, in some stories, she has nightmares and has to learn to trust people again.
One great 'Finnick Odair x Reader Fanfic' is 'The Capitol's Heart' where the reader character is thrown into the complex world of the Capitol and Finnick becomes their unexpected protector. It beautifully portrays the emotional turmoil and the budding relationship between them.
The fanfic 'Annie Cresta's New Beginning' is also quite interesting. It begins with Annie being rescued from the Capitol's clutches. The story then follows her as she discovers new friendships and a new purpose in life, all while still haunted by her past in the Games.
One fanfic that stands out is 'Finnick in the Shadows'. It gives a new perspective on Finnick, showing him as a more mysterious figure. 'Finnick's Final Stand' is another great choice. It's about Finnick making a heroic stand in a crucial situation. Additionally, 'Finnick and the New World' imagines Finnick's role in building a new world after all the chaos in the Hunger Games universe.
A lot of fanfics deal with his charm and charisma. Writers often expand on how he uses these traits to survive in the Capitol's cut - throat world. There are also themes related to his internal struggles. For example, how he copes with the loss of his innocence due to the Games and the Capitol's exploitation of him. And of course, love stories involving Finnick are quite common, whether it's a new relationship or the development of his relationship with Annie.
The best fanfics in this regard also have a strong emotional core. They capture the love, pain, and hope that Annie and Finnick experience. The writing makes you feel what they feel, whether it's the fear of being separated or the joy of a brief moment of peace together.