First of all, you need to stop thinking of us as being stationary and time as something that flows past us. Thinking of time in this way can never make sense, and more to the point, it has been shown to be incorrect. We travel through time just as we travel through space.

There would appear to be a maximum rate at which we travel through time, equivalent to the speed of light 'c' through space, otherwise the Lorentz equation for time dilation would not work in its established form, and experimentation shows that it does. In fact, the implication of the Lorentz solution is that we are always constantly travelling at the speed of light 'c' through the combined space-time environment, but as we slow in one direction we speed up in the other and visa-versa.

You can picture this by imagining that you are driving a car/automobile continuously at its top speed, let's say at 100 mph (because it's not a very fast car/auto). While you are driving directly North, moving at 100 mph in that direction, you're moving at 0 mph Eastwards or Westwards. However, if you start diving directly East, then although you're moving at 100 mph Eastwards your Northwards speed has now dropped to 0 mph. Finally, when you're driving in a direction somewhere between North and East, you'll then be moving at 100 mph, in that direction, but this means that you're now moving at less than 100 mph in both the Northwards and Eastwards directions. All we've done here is use North and East instead of space and time, and used a top speed of 100 mph instead of the speed of light.