Can a foreigner get vaccinated in Vietnam?

Unfortunately there are no vaccines for two of the diseases you mention.  Experimental dengue is being tested in the Philippines, Brazil and Mexico but there is currently no universally available vaccine.  Since you are Canadian:  https://travel.gc.ca/travelling/health- … ses/dengue 
Malaria is caused by a parasite not a virus, so for that reason, there is no vaccine.
Not on your list, Avian Flu outbreaks have occurred in Vietnam but the needed vaccine strain seems to change with each new outbreak.

I went back and checked your profile.  Your ability to speak Vietnamese should enable your search for a capable clinic.  I have never been to your town but I once spent a week in Cat Tien, just north of Qui Nhon, which I would expect is similar.  I can imagine that you will not find the services you want at home but will probably need to travel at least to Nha Trang.

I was wondering to see if anyone has tried to get a vaccine like the flu shot at a clinic in Vietnam before so I can get a feel for safety concerns, accessibility or if it's even recommended. For instance, I would never continue my immunotherapy shots in Vietnam because I know that doctors really don't have any sense when treating things like anaphylaxis and are oblivious to a lot of drug allergies. At least, that was my experience with government operated hospitals. I'm not sure if private ones are more well informed and wonder if they are affordable and available as well.

I have a script for malaria medication that can be take as a preventative measure if I feel the need to travel into a high risk zone. They said I can fill it in Canada or abroad but I have a hesitancy to get them in Vietnam for issues with verifying availability and authenticity. I've stay by the ocean mostly so I haven't seen a need for it yet. Dengue fever is the same and the risk of avian flu to be contracted by travellers are relatively low.

I feel that my north american healthcare team is just trying to generate paranoia and pushing me into purchasing ample amounts of drugs that I normally would not need. I have never known of any one that I've met in my travels or any local for that fact that has  ever contracted Japanese Encephalitis, meningitis, hepatitis etc.  I'm pretty sure that none of my relatives in Vietnam have been worried about such diseases before and have never vaccinated themselves so I'm not sure if it's even commonly available.

It's for such vaccines that you wouldn't normally find over the counter at a pharmacy that I am concerned about. For instance, the shots for Japanese Encephalitis alone set me back $600. I'm sure it would never cost that much in Asia, average people here would never be able to able to afford that .

Has any expat been concerned enough to even attempt to get vaccinated for such things in Vietnam before? Any past experiences or advice would be very helpful in helping me decided if I should try this in Vietnam or perhaps wait until I travel to another country with a less spotty health care system or even worry about vaccination at all in the first place.

I am surprised you are not getting replies to your basic question of where to go but if you work on searching this site there are many posts where people advocate for their favorite English speaking clinics.  I never went to any of these because I had an internist that I fortunately met at the swimming pool near my home.  He spoke fair English and served as my GP.  The times I went to hospitals for testing, I went with my wife without whom negotiating some local hospitals would have been a real nightmare.  Except for your rural location, you should be in a much better situation to negotiate health care.  One person you might contact by PM is 70 years old.   I hope he does not mind my taking the liberty of recommending him but, because of his wife's unfortunate illness, he has extensive experience with clinics and doctors, both English and Vietnamese speaking. 

As you noted, because of your coastal location, you likely should have no fears of dengue or malaria but you really should look out for and be vaccinated for both Hep A and Hep B.  Hep B in particular can cause permanent liver damage and even liver cancer later in life.  I knew a doctor in Hawaii who had liver cancer as a result of Hep B contracted while a US Army doctor during the war (before vaccinations were developed.)  Both viruses are prevalent in Vietnam and spread through restaurant and street food are the likely culprits. We were both going to be vaccinated for Hep B in Hawaii but found out through testing that my wife had a prior infection.  It was likely in childhood as she had no recollection, so her doctor had her take a single booster.   Check this thread:  https://www.expat.com/forum/viewtopic.php?id=595087 and some of the follow on links

Personally I have never been worried about dengue or malaria and never taken any medication, that said one of my friend did get malaria in Hanoi..  I
did got rabies shots and serum as my OWN dog did bite me, and that was not "cheap" and they did pump me full of vaccine.. I swear the injection place was more sore than the dog bite!.....

Technically the rabies shots are not a vaccine but an anti-serum.  They are after the fact but as soon as possible.