Hi Lucas,
I'm just a user, but I don't think they support this currently.
You can go to the genome's page, and click on the hyperlink number for "protein coding genes" and that will allow you to easily add all genes in the genome to your gene cart.
from there, if you go to the bottom of the page, you can add columns for extra annotation data to add to the table -- for instance, KO tag is under the third column (Function Field), "KEGG Orthology ID, Name and Definition".
Notice that if you go to a particular gene's page, there will be a lot more annotation data available (eg KEGG pathways), which cannot be exported in the gene table.
One workaround you could try is to download the "genbank-like" file for the genome.
you'll have to massage the data to suit your needs, so having some skills with something like SQL, R, Pandas (what I use), or Excel+VBA will be necessary.
These files seem to have a line for things such as KEGG module, COG Category, and Metacyc.
Another thing you could do is look at KEGG to see if you can download a table of all their KO tags mapped to KEGG categories & KEGG pathways, and then you could do a database join between the two.
(this would add on the appropriate KEGG category for each KO tag).
You'll probably have to clean up the KEGG ID tags (KO -- aren't these really K0, though?) in order to get them to match. I use regex-formatted searching within Sublime Text
I see there is a table of definitions for the KEGG module list under "Find Functions" >> KEGG >> KEGG Module List. You could export that, and then maybe first pivot each row by module type (do you know how to do a data frame pivot, or work with "pivot tables"? I use Pandas, but you could also use Excel, R, SQL, etc. I don't know what it means when things are in parentheses vs have - or + in front of them.
If you could somehow get each KEGG pathway into the function cart, you could profile all of them against your favorite genome.
Good Luck!
Matt Melnicki.
(Postdoc, Kerfeld Lab, LBNL & MSU)