Khronos is a variant spelling of Chronos. Chronos is often interpreted as being the same entity as Cronus. Cronus was the leader of the titans in our world, and I would speculate that the name has a similarly meaningful connection to the titans in theirs.
Might their literal goal be to revive or create new titans? To become titans, either literally or metaphorically?
I had forgotten the Titan reference… i thought they were somehow referring to thr god of Time… maybe i have that wrong tooo 
Titans could be a metaphor for their goals. . . they want to become a Titanic, unstoppable force of power in the world.
Kronos could also be referring to time more literally. We believe Myrddin could travel in time, and that would be an easy way for them to seize power fully and absolutely. Think about it. If you know where the High Crown will be at a certain time on a certain day, you could orchestrate a massacre in advance, and effectively take over. You could also find some way to compel those in power to do your bidding through magical coercion. Why stop at Lenore? If you can travel backwards and forwards in time whenever you want, you could also take over every other known country, and rule the known lands.
You might, also, cause another cataclysm. But who knows? We don’t even know if the Red Guard knows why the cataclysm happened. Time travel? Warping of the fabric of magic itself? Forbidden knowledge?
Kronos could aslo refer to something else that Azalea hasn’t brought to our attention. The other word is interesting too; why architects? They are designing a future? What else could they be designing? Why not builders or adherents?