Protons and positrons can theoretically flow as a current, as any flow of charge constitutes a current, even if it doesn't involve electrons. In particle accelerators, high-energy protons are accelerated in opposite directions and collide, demonstrating a practical scenario of proton flow. Additionally, in plasma, both electrons and positive ions flow under an applied voltage, with positive charges moving in the opposite direction to electrons. However, in solid conductors, positive ions are restricted to the crystal lattice, limiting their mobility. Overall, while protons and positrons can flow as a current, practical applications are primarily seen in specific environments like particle accelerators and plasmas.