I have worked on industrial burners (boilers) (with many different fuels), and been in the welding trades, and worked on many different types of appliances that use either natural gas or propane.
But when it comes to propane burners, and what we should need to know about them, especially when dealing with safety, I am no expert, so take what I have to say, with caution concerning this matter.
I have built many of my own small burners for my personal use.
My thoughts on this (take with grain of salt)]:
With a propane (or natural gas) if the burner is properly designed there should be no need for the flashback arrestors.
In a torch that is a totally different matter, I would use flash back arrestors. The torch (cutting or welding has a different design and it works differently and the conditions are very different from burners.
Acytelene will explode if pressurized (not sure at what pressure but somewhere above 15 PSIG), With a much higher oxygen pressure, and a mix of acetylene and oxygen and the back pressure of a flashback or sustained back fire, in the torch you can be standing next to a bomb trying to melt a little gold. so use flash back arrestors and check valves on your torch.
Propane under Normal working pressure does not explode (like acetylene will) it can be compressed to a liquid, as that is what is in your tank (the liquid under pressure drops to a lower pressure environment in your burner to become a gas(actually gas fill the small volume of the tank inside but lets not get too technical here).
In a properly designed burner, the propane is forced through a small diameter orifice (very small hole say a # 56 or #62 drill for example) the gas flows into a stream of air (from a blower or from the venturi effect of the burner itself) or even a stream of oxygen. The burner is not really under much pressure (even with a blower, (compared to a torch and its design). So the likely hood of mixing fuel and oxidizer (in the gas line or in the tank) is not likely to happen (my opinion only). If it did get oxygen or air into your tank I do not believe there would be much of a problem (again keep the salt handy).
As far as burn back or flash back in the burner, here any safety device would never be a bad idea.
But I really cannot see the burn back entering the fuel line or the tank through the orifice in the burner design (torches again is a totally different story).
A flashback is different than a sustained burn back or backfire.
For a moment lets discuss torches (I may get back to the burner).
In A torch:
Most of the causes for a flashback or a burn-back (back fire) are normally operator error, using the torch wrong (overheating), damaged (seats), loose or leaky fitting or damaged parts in the torch.
Burnback or backfires are normally less dangerous (than a flashback) the burning back of the flame inside the torch tip (Loud popping or snapping noise) as the flame goes out, will rarely get past the mixing valve to (create a flashback).
The Flashback can be much much more dangerous! here the flame (similar to small high-pressure explosions) burns back past the mixing valve (sounding like squealing pigs, or hissing snakes) as the flame pops out the torch tip spews clouds of black sooty smoke, if you get flash backs something is seriously wrong with the torch (need repair of faulty condition) or it is from how you are using it (overheating, too close to work, using wrong pressure setting...).and as mentioned earlier with acetylene it becomes explosive somewhere above 15PSIG (note the red line on yer gauges).
The burner (of course this depends on the type, but for what burners most all of us on the forum would use) is much different from the torches we use.
The burner will not suffer the same issues, as the torch.
My recommendation is Always Use check valves and flashback arrestors on your Torches.
Although a flashback arrestor and a check valve could never hurt and would be a smart safety feature, the flash back arrestor is not totally necessary on a "properly designed burner.
Now saadat68,
As far as your burner and what I can tell from the picture, I do not see any obvious safety issues.
But as far as the design I see some things I would change, (they may not be needed as I have not used or tested it), (so again we may need some salt, with my words), the delivery pipe looks very long (may or may not be a problem, but I feel the pipe from the blower should be bigger in size (you want a good volume of air, and little restriction, (maybe even sizing it as big or bigger than the fan blower outlet).
The galvanizing (zinc coating) from galvanized pipe (if that is actually what you are using) is a big NO NO, Zinc burns and oxidizes easily and emits white spider webs into the air. I have had night sweats chills where you feel like you are dying from welding on Zink coated steel (galvanized steels). Use black iron pipe.
I am no expert by far, and only can go on what little I know or believe, so take it for what it is worth (not much), do your own research. just my own opinion on the matter.
My safety is in my hands, and your safety is of yours, my friend.
A few Tidbits on propane, I would look for more myself and study as much as I could on the matter.
https://gashosesandregulators.com/propaneregulatorfacts.php
http://www.harrisproductsgroup.com/en/Expert-Advice/Articles/Flashback-Arrestors.aspx
Propane approximate vapor pressure of liquid at various temperatures:
-20 deg. F ----10 PSIG
0 deg. F ------23.5 PSIG
+20 deg. F ----40.8 PSIG
+70 deg. F ---109 PSIG
+ 110 deg. F---197 PSIG
Note also the more volume of gas delivered from the tank the colder the tanks get( multiple burners, large burners long use time a large volume of flow), it is not uncommon for the tanks to freeze or develop a frost from the refrigeration effect of the liquid changing to a gas (high-pressure liquid to a low-pressure gas) where it may be necessary to sit propane tank in heated water or use a heater blankets...