One could say an example of going with the flow is being open to changing times. Pushing on when feeling lost, or being uncertain of the what the future will bring and adapting. "Going with the flow" and taking time to see things through, in most cases, eventually brings success. Other examples include, living in the now, transitioning with changes as they come to you, or having a goal and understanding that winding down the river is how to get there.
Pranayama is the practice of breath control(prana-yama), and a vital component of yoga. Breath gives life force, it also inspires flow, similar to the tide or ebb and flow of waves on a beach.
In Vinyasa yoga or Ashtanga, flow is the rule. Keeping with the breath, without breath, the practice feels forced, labored, and unsustainable. During yoga practice fluctuations of the mind are minimized and the breath is insync with the cadence of movement. Flowing in and out of postures, always letting go, pausing, and taking back no goal or end, just flow.
Pranayama or breathing exercises like deep diaphragmatic breathing, benefit the parasympathetic as well as the central nervous system by inciting the relaxation response. Holding the breath or shallow breathing creates tension, both mentally and physically.
Similar but scientifically superior to other forms of exercise, yoga builds its foundation on breath. One could say breath is 90% of a yoga practice. Without smooth controlled breathing, going with the flow would not be possible.
So while life is unpredictable and can make, "going with the flow" difficult, the balancing effect of pranayama and yoga practice allows the mind and body to relax, re energize and flow.
"Let it grow, let it grow, let it blossom, let it flow." Clapton