Solo/duo is only for one/two people and in theory focuses on individual skill.
Flex is for 1, 2, 3, or 5 people, and in theory focuses on teamwork more than individual prowess, so the idea is you can queue up with your friends and have coordinated plays. 4 man premades are disabled because it's often a particularly bad experience for the 5th person, as the 4 premade may be on their own comms and may not communicate at all with the 5th, or if they do communicate it's more "do this, we say so" and it can be more of a bully situation.
Flex is a bit of a fiesta in practice since theres a lot of variance in skill level in any given game, so it can feel a messy as normals, where diamond skill individuals can be in the same match as bronze skill individuals. (Again the theory is that maybe peoples extra teamwork and coordination could allow lower individual skill players outplay uncoordinated higher skill people...but it's messy.)