The multieffect bioconvective heat transfer in porous media is essential for many technological applications. However, the literature governing practical applications is very scarce. The bioconvective transport of magnetohydrodynamic cross nanofluid carrying oxytactic microorganisms across a flexible cylinder with velocity slip, viscous dissipation, thermal radiation, and chemical reaction with a heat source in Darcy–Forchheimer porous medium is predicted in this piece of work. The random movement and thermophoresis processes are revealed by the Buongiorno model. Using a suitable similarity transformation and boundary layer approximation, the simplified model equations are converted into coupled highly nonlinear ordinary differential equations (ODEs). The resulting ODEs are dealt with numerically utilizing the BVP4C and the shooting method with predetermined thermal radiation, heat source, chemical reaction, and so forth parameters. The velocity field is inversely influenced by the Forchheimer number and porosity parameter. The Sherwood number is significantly influenced by chemical reactions. For heat source parameter (S) and increasing radiation parameter (Rd), the Nusselt number increases and convection is shown for the value of Rd near about 3. Overall, this study will help researchers in science and engineering to understand the intricate and multieffective dynamic system and industrial applications like microbiology, and biodynamical systems, biological tissues, biofilms, soil, or filter media.