How can I stabilize flowering tube onyx?
You may have some luck with stabilizing it as though it was a slab. Using an epoxy in acetone method:


Dissolve epoxy in acetone
Submerge rough stone in the epoxy acetone mixture
Seal up container so acetone does not evaporate
Leave in mixture for at least a week
Remove from acetone and let dry for at least another week 


Mindat has some good instructions along with other methods



The important detail is this method relies on diffusion. When you have a slab your path length is relatively short, so the epoxy can diffuse in fairly quickly (days). As you make the material thicker the time increases. If you have a piece of rough that is fairly narrow in one dimension, you're in luck, treat it as a slab, diffusion won't be slowed down by rough edges, indeed it will be slightly faster. Where you're going to run into problems is with a thick piece of rough material that resembles a sphere. In this situation you may want to go at it in multiple passes as follows:

Let's say that your rough material is sphere with a diameter of six inches. Additionally you've determined that you can "completely" stabilize a slab that is one inch thick.

If you follow the same procedure with the rough material, you can "completely" stabilize the outer 1/2 inch of it. At which point you could cut off slabs as circles of a sphere:



of 1/2 inch thickness.
The process could be repeated to allow for a second, larger, slab to be produced.

I would probably sacrifice the first layer, as it is typically irregular to begin with, making a poor slab. Or, because I am impatient, I would slab the rough and accept what breaks as broken and stabilize the usable parts as slabs.

Note: It has been years since I've made a cab and my knowledge of stabilization techniques is from research only, I have not tried these techniques myself.