Another option is to check out some Naruto - focused fan communities on social media platforms like Tumblr or Reddit. Some users might share or recommend good Akatsuki - Naruto yaoi fanfictions there. You can also post a request asking for such fanfictions, and fellow fans might be able to point you in the right direction.
You can try fanfiction websites like Archive of Our Own (AO3). There are a large number of Naruto fanfictions there, including those with Akatsuki and Naruto in yaoi relationships. Just use the search function and type in relevant keywords to narrow down your search.
Fanfiction.net is also a good place to look. However, the tagging system might be a bit different. Look for the Naruto section and then search for Akatsuki and yaoi related tags. But be aware that the quality of the fanfictions can vary greatly, so you might need to read a few to find the ones that suit your taste.
Chapter 488, "You Must Be the Captain Then!", is the clearest early answer because it turns Shang Shaojing's situation into a concrete plot event. It opens with Lose face?" Nina's voice rose sharply, "We're already at a dead end,...
Chapter 676, "Third Uncle Will Buy It for You!", is the clearest early answer because it turns Shen Lan's situation into a concrete plot event. The chapter gives readers a real answer by opening on Jiang Zhao Yuan felt somewhat embarrassed by such a direct revelation.
Chapter 597, "Uncontrollable Things Still Happened", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Gu Yu's disappearance couldn't be related to the secret of this...
Chapter 374, "From Now On, Jiang Li Calls the Shots in Golden Sand!", is the clearest early answer because it turns Jiang Li Calls's situation into a concrete plot event.
Chapter 649, "Where Did the Wild Wolf Come From?!", is the clearest early answer because it turns Jiang Cheng's situation into a concrete plot event. It opens with Several people successively lay down in the tent, and before long,...
Chapter 480, "I'm the Guest, Give Me 500 Points", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. The chapter turns that into something concrete by moving from Team H delivered the seafood feast as promised.
Chapter 447, "Going Viral on the Internet", is the clearest early answer because it turns Jiang Yan's situation into a concrete plot event. It opens with Old Sir Jiang: "...." His face had grown even worse. and closes on She quickly grabbed He Wen's laptop and indeed saw that the various....
Chapter 517, "Master Jiang Opens the Third Eye Online", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. It opens with Mu Ye was completely caught off guard and stood there dumbfounded for...
Chapter 256, "Bonfire Feast", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. Early on, Turning around, Jiang Yan and Zhao Lang found their heads had been.... By the end, I was dazzled seeing Jiang Li trending today." Next door, Su Yinwan....
Chapter 851, "Peace Charm", is the clearest early answer because it turns Kexi's situation into a concrete plot event. A useful checkpoint is the way the scene starts with She initially came with the expectation of becoming the Gu Family's...