You may be speaking of the subjective experience of time, which is not a physics question, but rather a psychological one. Otherwise, the last paragraph of your question doesn't seem to make any physical sense. Time is an arbitrary standard by which a motion or a process is measured relative to other motions and processes.
For example, you can synchronize your time standard to this: http://www.time.gov. Each second the clock ticks corresponds to 9,192,631,770 cycles, the natural resonance frequency of a fountain of cesium atoms isolated from other radiation, cooled nearly to absolute zero, and energized by microwaves at the National Institute of Standards and Technology.
The cesium atom has a large difference between spin states of the single electron in its outer shell. When the spin state is altered it emits a photon and glows. When a fountain of energized cesium atoms are glowing in unison, the energy required to maintain the glow has a frequency of 9,192,631,770 cycles per SI second. Here's a more accurate explanation: http://www.nist.gov/pml/div688/how-nist-f2-works.cfm.
The precise apparatus that measures the frequency that produces the glow neither gains nor loses one second in 300 million years. So for practical purposes, it doesn't have a rate of change, which makes it an ideal candidate to measure the rates of change of other processes.
You may be thinking, "but what is the absolute substrate of ultimate duration through which the 9,192,631,770 cycles travel?" The carrier of this particular measure of duration is a fountain of cesium atoms. I don't know of anyone who's found anything beyond that.
Even as regular and unchanging as a cesium clock is, if you were to whizz it around the Earth at a relativistic speed, the cycles measured by that clock would not correspond to the cycles measured by an identical clock motionless relative to it. Two clocks ticking at the same frequency will not agree, depending on their relative motion and position in the Earth's gravity field. This prediction of special relativity has been confirmed by experiment: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html.
No universal "flow" of time has ever been discovered outside the space-time manifold, to my knowledge. Time may be considered a way to compare motion and process, the attributes of matter and energy and space.
One great mystery, which might be the reason it's easy for people to think that time has an independent flow, is the Arrow of Time. The past seems a different world from the future. The Arrow of Time was explained by Boltzmann as the 2nd law of thermodynamics: One can distinguish a past from a future because the entropy of any thermodynamically isolated and mechanically closed system, and of the entire universe, will always increase from the past to the future. This is an attribute of matter, energy, and space. But there is no "flow" of entropy separate from matter, energy, and space. Likewise, time is a way to compare motion and process. It is not something apart from matter, energy, and space.