Does cannibalism among other animal species also make them more susceptible to get a prion disease, and are there distinctions between mammals doing so and other orders like reptiles, birds, fish etc.?
It is perhaps worth looking into more historically established prion diseases in noncarnivorous animals, like sheep. If prion diseases were only transmitted by consuming prion-rich brain tissue, then they should be extremely rare (produced via unique misfolding events or mutations in affected individuals) or completely absent in wild herbivores and domestic herbivores which are not being fed meat meal.
In fact, I mention scrapie because it predates the practice of supplementing livestock feed with meat-derived protein. (The first documented mention of the disease dates back to about 1772 and mentions that the disease is about 40 years old at that point.) As it happens, the earliest mention of livestock feed or feed supplements being composed of meat and bone meal I can find dates to about 1890. Prion diseases also appear in wild populations of elk and deer in the form of Chronic Wasting Disease, currently a big problem in the northern US and Canada, as well as in cattle and sheep.
So how did scrapie come to be such a problem for European sheep farmers?
Well, for one thing, scrapie (and CWD) can be transmitted via ectoparasites. But the most common culprit probably lies in the soil. It turns out that infectious prions can survive for years in soil once they're deposited. Not only is the decomposition of a carcass a way to infect the soil with the misfolded prions, but CWD proteins are also present in the excreta of infected animals and even antler velvet.
This is a problem, because both scrapie and CWD can be acquired simply by consuming infected soil or grazing on grass containing it. This is most likely the most common way that these prion diseases are acquired naturally--not cannibalism at all, or at least not the sort we commonly think of! It's a simple fecal-oral route of transmission, albeit one with an alarmingly long potential incubation period.
An individual (animal or human) acquires a prion disease when they consume meat that contains prions (proteins that are mishapen enough to drastically change their functionality), which subsequently causes proteins within the individual to misfold into the same shape as the prion, resulting in a whole slew of problems.
As of right now, there is little knowledge of where prions come from/how they're formed. Also, there is little knowledge of how inter-species infections/transmissions occur. Researchers are currently investigating various combinations of inter-species transmissions, such as humans eating infected horse meat, or cats eating infected chicken meat, but still know only very little about this phenomenon.
To say which species have higher rates of prion disease when looking at a cannibalist communities within that species, I don't think we're anywhere near close to making those conclusions, and the same goes for inter-species transmissions.
All the best.