Having made this point way too many times before, it almost seems futile to keep making it, but the actual physics makes much more sense if we think of it, not as some 'flow' from past events to future ones, but the process by which events go from being in the future to being in the past. Ask yourself, does the earth 'flow,' from yesterday to tomorrow, or does tomorrow become yesterday because the earth rotates?
As Davies points out, "When we observe the world, what we see is an apparently consistent and smooth narrative, but actually the brain is just being bombarded with sense data from different senses and puts all this together."
The "apparently consistent and smooth narrative" is that personal neurological perception of a sequence of events, ie. prior to subsequent. It, that 'flow,' is the narrative , past to future perception, not the constant rearranging of 'data' by which those events are being created and dissolved! The events are flowing through our perception, future to past, not us flowing from past to future, because we only exist in what is physically real and it doesn't move along any metaphysical dimension. Duration doesn't exist as an external 'dimension' to the 'point of the present,' but is the condition of what is present between particular events.
If we understand time in this sense, it is no more mysterious than temperature, as a basic effect of action, ie. change. Keep in mind that temperature is every bit as foundational to reality as change/time. From elemental background radiation to the process of entropy, where energy seeks that thermal median.
Different clocks run at different rates because they are distinct actions. Reality doesn't branch out into multiworlds because it is the collapse of possibilities that yields actualities.
Now I can understand why those firmly wedding to certain physical theories, such as anything depending on a physically real spacetime(not just correlations of measures of duration and distance), may not wish to consider this point, but those less wedded to orthodoxy might want to think it through, just out of curiosity's sake.
Regards,
John M