"The flow of time is an illusion...The reason that it is an illusion is when you stop to think, what does it even mean that time is flowing?"
"Time of course exists. We measure it with clocks. Clocks don't measure the flow of time, they measure intervals of time. Of course there are intervals of time between different events, that's what clocks measure."
Time according to Davies is what clocks measure, which are intervals of time. Time is therefore intervals of time, or time is time, which is circular. We often define time as being time in lots of complex recursions, which of course are all circular but certainly true. It really is not that useful to say that time is time, though.
Of course, time is an axiom and therefore is really not like any other single thing. However, time as an axiom can be defined by the other axioms of the universe. In fact, time is defined as both an interval and as an integration of those intervals, which is an action. The key is to not use time to define time.
Rather, define an interval as matter. The mass of a grain of sand in an hourglass, for example, represents a moment of time as matter. The accumulation of those grains represents the integration grains in time, which is the action of that clock. Thus, time is formally defined as the differential of action with matter, the accumulation of matter divided by the matter of a moment.
It is very useful to define time as the differential of action with matter. Not only is that dimensionally correct, it is actually a universal definition of a clock. The atomic clock is formally set to record 9,192,631,770 or nine billion cycles of the cesium 133 atom hyperfine resonance per second. Each moment of the atomic clock then represents a very small energy equivalent matter of 1.1e-41 kg. This is a matter moment and the accumulation of these moments as matter over one year amount to about the action of three hundred hydrogen atoms.
Now, that is finally defining time without using time!