Re: What criteria would support treating prokaryotes as several kingdoms?

The short answer is that any criteria that would show that there are several groups of prokaryotes that are close to equidistant from each other and as distant from each other as the kindoms defined among the eukaryotes (protists, plants, fungi, animals) are from each other, could serve as criteria for treating each of these groups as its own kingdom.

We now have the ability to sequence DNA genes and even complete genomes of both prokaryotes and eukaryotes, and this gives us much more information, much more rapidly, than any of the physical appearance and biochemical traits that were used in earlier studies, to judge how closely or distanntly related groups of organisms are to other groups. In almost all cases, the DNA sequences serve to re-confirm the classifications done prior to the discovery of DNA sequencing. For example, the Salmonella and Escherichia groups of bacteria were both Gram-negative rods that shared many biochemical traits and were thought to be related to each other, and DNA sequences of their genes confirms this. Studying 2D protein gels and using serological methods are other methods that were widely used before DNA sequencing was readily available.

So far, there have proven to be just two main groups of prokaryotes that are roughly equidistant to the eukayotes and to each other. They are the Eubacteria, which includes almost all of the bacteria that are commonly known to man; and the Archeabacteria, which tend to be found only in strange and extreme environments such as thermal vents on the ocean floor or hot springs near volcanic activity. It is my understanding that it was Carl Woese who proposed three divisions of life at a level higher than the kingdom:

Woese CR, Kandler O, Wheelis ML.
Towards a natural system of organisms: proposal for
the domains Archaea, Bacteria, and Eucarya.
Proc Natl Acad Sci U S A. 1990 Jun;87(12):4576-9.
PMID: 2112744

But others may have made this proposal, as the study of archaebacteria was already well established before 1990. See for example:

Tu JK, Prangishvilli D, Huber H, Wildgruber G, Zillig W,
Stetter KO. Taxonomic relations between archaebacteria including 6 novel
genera examined by cross hybridization of DNAs and 16S rRNAs.
J Mol Evol. 1982;18(2):109-14.
PMID: 6178834

The terms "domain" and "urkingdom" have been used to refer to these three main groups of life forms. And at least one group of reseachers has proposed four main groups; adding the Eocytes:

Lake JA.
Ribosome evolution: the structural bases of protein synthesis
in archaebacteria, eubacteria, and eukaryotes.
Prog Nucleic Acid Res Mol Biol. 1983;30:163-94.
PMID: 6420842

Lake JA.
Evolving ribosome structure: domains in archaebacteria,
eubacteria, eocytes and eukaryotes.
Annu Rev Biochem. 1985;54:507-30.
PMID: 3927820

Within any one of these three major groups, there are subgroups. Eukaryotes are obviously very diverse, including fungi, plants, animals and various single-celled organisms that are clearly (or not so clearly in some cases) not fungi, nor plant, nor animals. Prokaryotes are not so visibly diverse. They are all so microscopic that they often look similar even when they are very different by biochemical or DNA sequence evidence. But within the prokaryotes, divisions are becoming very easy to identify via DNA sequencing and the analysis of the sequences which is called phylogenetic analysis. It started with sequencing 16S ribosomal RNA, which was simple to purify and sequence, but now it is becoming common to sequence the complete genomes or prokaryotes. However, because of the long history of studying 16S ribosomal RNA, it remains a favored region of the genome for initial characterization of potential new organisms. For example:

Kim H, Honda D, Hanada S, Kanamori N, Shibata S, Miyaki T,
Nakamura K, Oyaizu H.
A deeply branched novel phylotype found in Japanese paddy soils.
Microbiology. 2000 Sep;146 ( Pt 9):2309-15.
PMID: 10974118

In general, it seems that the more we learn with science, the more we find there is more to learn yet. We also find that nothing is as simple as our first theories made it seem. Atoms are now being theorized to be made up of subatomic particles, which in turn might someday be explained by string theory, for one example. In the case of classifying life forms, we increasingly find life forms that don't easily fit into our current classification scheme. Horizontal gene transfer, for example when a virus carries a gene from an insect into a mammal, or when a bacteria picks up genes from a plant it lives with, present another problem.