I like giving Conan a few levels of rogue (no more than 3!) simply for the class abilities.
His athletic ability is beyond extraordinary, particularly in the area of climbing. His scaling of the Elephant Tower is matched only by Taurus of Nemedia, who is called a Prince of Thieves. He scales sheer cliffs and walls like it ain't no thang, suggesting he has climbing ability far beyond simply being trained and strong. Gaining double-proficiency bonus on Athletics from rogue expertise seems valid; if you go as far as 3rd level rogue, you also get Second Story Work from the Thief sub-class (full movement when climbing) which seems appropriate for several of the canon stories. As a 1st level rogue gets expertise in two skills, I'd probably go Survival for the other one. Conan exhibits the ability to survive far longer than normal men in hostile terrain (or when nailed to crosses). You could argue this is just a factor of his high Con saves, but he consistently shows terrific ability as a tracker, hunter and woodsman (Beyond the Black River, Black Stranger, Jewel of Gwahlur, and other tales). So, expertise in Athletics and Survival.
Sneak Attack is questionable, but he does take out a number of people quickly and quietly when attacking from surprise (the doorman and the innkeeper in Shadows in Zamboula, for example). So, it's not beyond reason. Cunning Action is more justifiable; he is sometimes described as having the speed of a great cat, and a surprising number of Conan stories involve him evading and fleeing from opponents (usually hordes of picts, or creatures-from-beyond like the iron statues or the black ones). Being able to disengage or dash as a bonus action would seem to be justified from many of the canon stories.
So, really, it's just about that 3rd level of Rogue, for me. Picking up Second-Story Work is nice, as it models Conan's outstanding climbing and jumping abilities quite well. Barbarian and Fighter class abilities aren't helping so much in those areas. Fast Hands is less important (he's not a lock-picker!), although Use Item as a bonus action could be appropriate to model events in some of the stories. Conan does make fairly extensive use of terrain features and objects in a lot of his adventures. But I could concede the 3rd level of Rogue, in a debate. Assuming he's a Barbarian 6 / Fighter 11 for the other levels, I'd give him a 12th level of Fighter for the ability score improvement or feat. Given his ability array, he needs as many of those as possible - although he's not going to be a stat buy PC anyway. R E Howard clearly rolled "best 3-of-9d6" a whole bunch of times until he got the array he wanted...
