Archetypally, the male is about forward motion and problem-solving. The male mode of thinking is logical and procedural, A -> B -> C -> D all in a straight line to a desired goal. It typically involves exchanges: I take this and pay that. It is definitely not “going with the flow.” If anything it’s the precise opposite.
The female mode, on the other hand, is characterized by what the Taoists call wei wu wei, literally translated as action no-action. It means passivity within one’s own nature, so that while the body may be very active, the mind is passive and watching. It is based on deeper forms of connection than formal logic, typically intuitive in nature, involving jumping from A -> D without intermediary steps using unconscious pattern-recognition and analysis. As you can see, this is almost literally what’s meant by “going with the flow,” and indeed the Tao Te Ching often compares this mode of being to the behaviour of water.
Now, male and female have nothing to do with genitalia. We all contain both male and female (the Anima being the female-in-the-male and the Animus being the male-in-the-female). But culturally, we have a bias for training those with wombs to adopt the female nature and those who plant the seed to adopt the male nature. As a result, most men tend to think in male thought patterns.
In most successful relationships, one person adopts the male role and the other the female role. It may be, given your description, that you serve the male role in the relationship, moving it in a desired direction, while your boyfriend is content to serve the female, flowing like water and bending like a young sapling under pressure. If this is the case, he may be quite content to allow you to steer, watching passively and enjoying the ride.
In answer to your question, no, it’s not typical for men to “go with the flow.” Not in our culture, anyway.