I suspect the answer is theoretically "yes" because basic chemical makeup and temperature of a human brain is not dissimilar from a canine brain.
So the question is, can the canine brain become infected with the amoeba? In humans, the infections have come from swimming in contaminated water and taking the amoeba in through the nose or through use of a Neti-Pot.
The term "brain-eating amoeba" makes the amoeba sound like a tiny
zombie stalking your skull. But brains are accidental food for them.
According to the CDC, N. fowleri normally eats bacteria.
The good news is that if you were to drink a glass of water
infested with N. fowleri amoeba, you would not get a brain infection.
It infects people by getting into your nose. Source
So the risk comes from ways your dog can get water in the nose. And then, even if the water gets into the nose, only a small percentage of time will that water contain an amoeba, and even if it does contain the amoeba, there is a good chance the amoeba will not make it to your dogs brain, but instead end up cycling through his system the way the rest of the water does.
How Do Amoebas Get in the Brain?
Studies suggest that N. fowleri amoebas are attracted to the chemicals
that nerve cells use to communicate with one another. Once in the
nose, the amoebas travel through the olfactory nerve (the nerve
connected with sense of smell) into the frontal lobe of the brain.
How Frequently Do People Get Infected by Brain-Eating Amoeba?
Even though N. fowleri amoebas are relatively common, they only rarely
cause brain disease. N. fowleri disease is known as primary amoebic
meningoencephalitis (PAM). It occurs from zero to eight times a year,
almost always from July to September. SOURCE
It's a rare occurance, and it mostly happens in the summer. The best thing to do is not stress to much, avoid allowing your dog to swim in untreated warm freshwater (SOURCE: see How Can Infection with Naegleria fowleri be Prevented?) and be careful while giving him a bath, and your dog should be fine. As noted in one of your links, there are many experts who believe that it is not possible for a dog to even get the parasitic infection in the first place. I asked my vet friend, and while she was unwilling to commit to the opinion that it was impossible, she stated there was enough differences in the canine nasal cavity from the humans, that she believed the incidence of infection would be drastically reduced.