Minato is fast. His teleportation is instant and his reaction time and speed is enough to be able to teleport to dodge almost anything. But there in lies his flaw, its his reaction speed that is his own. His physical speed is great, but it is not the reason why he is truly fast.
The Raikage on the other hand is all physical speed and he has mastered Body Flicker. He uses his Lighting style to enhance it to incredible proportions, resulting in him being one of the fastest Shinobi. He is one of the few people specifically mentioned on the Body Flicker Wiki page for his increadible skill with it.
It is those 2 different techniques that explain why Minato did not use Body Flicker. Minato is physically slower than the Raikage. He has top tier reaction speed, and his teleportation is instant, but his running speed is not. To use Body Flicker against the Raikage would be like an average runner trying to outrun an Olympic Sprinter. He would most likely loose every time and get caught, resulting in him teleporting anyway for a waste of stamina and chakra. The Raikage knew this.
TL;DR Minato using Body Flicker would always loose to the Raikage and his top tier mastery of Body Flicker that has been enhanced by lighting style to be even faster. Minato could only outrun him by using teleportation. Any attempt to use Body Flicker would result in him loosing the footrace.