Smartphone addiction and academic burnout are typical psycho-behavioral problems among adolescents. Extant studies tend to examine them from a single-problem perspective, while research on their co-occurrence is lacking. Moreover, research has been prone to focus on the impacts of the negative sides of smartphone use on the two problems, ignoring the influences of its positive sides. This study applies latent profile analysis (LPA) to probe the co-occurrence patterns of smartphone addiction and academic burnout and the role of both the negative and positive aspects of smartphone use, namely smartphone stress and digital flourishing. Analytical data were from 810 adolescents from secondary schools in China. LPA revealed three co-occurrence patterns: a No Addiction and Burnout Group (34.2%), a Low Addiction Risk and Medium Burnout Group (48.6%), and a High Addiction Risk and Burnout Group (17.3%). Smartphone stress was positively associated with the co-occurrence of the two problems, but digital flourishing can weaken its effect. This study is the first to examine the effects of both the negative and positive sides of smartphone use on the concurrence of smartphone addiction and academic burnout. It has implications for intervention schemes.