DESTINY+ is an upcoming JAXA Epsilon medium-class mission to be launched in 2024. The spacecraft will demonstrate advanced technologies, including highly efficient solar electric propulsion to enable deep space missions with lower costs and higher frequency. As the nominal science mission, the spacecraft will perform a high-speed flyby observation of (3200) Phaethon. Visits to several other asteroids are part of the extended mission. This paper presents the mission design and flight operation overview of the DESTINY+ mission. Epsilon S launch vehicle has the capability to insert the spacecraft into a near geostationary transfer orbit. The spacecraft will raise its orbit by solar electric propulsion in a spiral-shaped trajectory that will take it to the vicinity of the Moon. A number of lunar gravity assists will allow the spacecraft to fly to an interplanetary orbit that will take it to multiple asteroid flybys. In addition to the mission analysis, this paper includes an operational feasibility study, as it is highly coupled with system constraints.