Will a Shimano Dura-Ace 9000 55-42T crankset be compatible with my current Shimano 8 speed 11-28T cassette?
The purpose of this change is for Time Trialling.
If you ask shimano, they will say this won't work. But in my experience with 11spd cranks and 9 speed chain cogsets, it always works well enough. I've never had any significant problems using an 11spd crankset with 9 speed chain and 9 speed front derailleurs.
The difference between 8/9/10/11 speed chain is the external width, not the internal size. The only difference between an "11" speed crank and an "8" speed crank is a slight narrowing of the spacing between the chainrings so that the narrower 11 speed chain won't fall in between. The dimensions of the chainrings are the same since they all have the same internal width. I would not expect any problems using that crank with 8 spd that can't be solved by switching to a 9 or 10 speed chain.
The biggest problem you will have is likely getting the derailleur high enough to clear a 55t chainring. If you have a frame mount derailleur, most of those will only go up to a 53t without grinding the derailleur mount.
You should be able to use that crankset with an 8 speed cogset. If you do run into issues with the chain angle rubbing in the small/small gear, you can try using a "smaller" chain (i.e.) 9 or 10 speed.
Nominally no, an 11 speed speed crank will not work with an 8 speed drivetrain.
As the number of speeds (number of cassette sprockets) increased as new groupsets were released, the sprockets were narrowed and moved closer together. The outside width of the chain was also progressively narrowed so that they worked with the narrower sprocket spacing. This also meant that crank chainrings had to be moved closer together. An 8 speed front derailleur and chain will not shift at all well on a 11 speed crank.
Other things you should bear in mind if you are serious about a 55/42 crank. You may not have enough chainstay clearance for the bigger rings, and you will need to check that your front derailleur will move up enough - some braze-on clamps don't have enough adjustment.