How quickly is the Earth shrinking? Except for ice, acetic acid, bismuth and gallium and a few other things materials generally shrink when they cool and solidify, so I'm pretty sure Earth has as well.

It probably wouldn't be measurable over a period of years, but models of the Earth's current and historic rates of heat flow can probably be used to estimate a rate of change of Earth's average size and possibly oblateness.

Right now WGS84 uses 6378137.0 meters for Earth's equatorial radius and a flattening at the poles of about 1/298.257222. 

How fast might those change over any given million years?
(Related to answers to the question Thermal expansion of Earth, which I only realized after having saved this answer. So, in principle, a double post, but I was asked to undelete :-))
Earth's thermal history may give some hints -- not sure if this is an actual answer to the question. It seems like Earth's radius depends on the layering of mantle convection, and that though there were significant changes during the Archean Eon and earlier, the current and recent (since the late Archean) shrinking rate is slow (a reduction of 12km in radius in 2.5Gy).
Source:
Expanding-contracting Earth by Tsuchiya et al. 2013 in Geoscience Frontiers

Questions that remain:
What about the core ?
And is mass loss or gain from astronomical processes significant enough ?
I would like to add that WGS 84 is a reference ellipsoid, and height values can be (are) given as positive or negative numbers. They can be updated every now and then by satellite. Also, I would assume that tectonic processes or local anomalies may by far outweigh any signal from thermal shrinking over the course of next centuries or even millennia (speculation).