For my question, the dragons are no taller than the average human, and they would have about the same intelligence as a human as well, their colouring is grey-ish blue, and they have access to all similar kinds of weaponry found in WWII and they have no helmets or clothing, but they still have protective padding, like water canteens and simple medical provisions with them (that they don't have to carry in their hands). They can fluently communicate between themselves and regular people. The dragons are in an army along with humans they are up against an opposing army entirely composed of humans. And both sides have relatively equal quantities of tanks, AV's, warships and planes.
Assuming it's the fire-breathing and flying type of dragon it kind of depends on what part of the war you talk about (early or late) as the war gear available changed drastically during this time period.
Throughout the war they will have two skills that will be extremely valuable. If they can fly they will be exceptional at gathering intelligence compared to regular aircraft as they have a tiny radar profile, a tiny profile to shoot at and I wanted to add they would be far more silent but due to the wingspan and how loud small birds actually already are when flying I have to scrap that one.
The second skill they'll have is urban combat. Their fire breath (if they have it) would work a lot like a molotov cocktail, allowing any dragon that gets close to the air intake of an enemy vehicle to cause it to heat up from the inside and catch fire. There's also a nice advantage is being able to enter a room just after a large plume of fire causes your opponents to step back and perhaps flee. After all it could be someone wielding a flamethrower who's about to cook the entire room and you better get out of there fast.
Fighting non-dragons is also a huge advantage. Most living things have a natural resistance to killing their own kind or even causing permanent damage to others of their kind. This caused people throughout firearms history to fire over their enemies rather than at them as even in those life-or-death situations they are unwilling to actively kill the opponents. Modern armies drill specifically to replace this reflex with one where the soldier actually fires to kill, with all the psychological consequences afterwards. But your dragons likely don't have this compulsion when faced with humans and fire more accurately. The unfortunate side-effect is that it'll likely be fired upon more accurately as well.
Really, really effective as code speakers
Yeah, we're not going to do something silly like waste them on dangerous jobs or anything like that when there's so much better of a use we can use them for. See, in WWII, because of it's potential, intelligence was more valuable of a commodity than any one soldier's life - so much so that the fact that the Allies had cracked Enigma cypher was occasionally concealed by letting German run successful mission because of how concerned the Allies were about keeping it hidden. Being able to talk without any concern of the other side cracking the code is a huge advantage for one side to have.
Take, for instance, the Navajo soldiers. They spoke Navajo, which to be fair, is said to be a language that is apparently impossible to learn if you aren't a native speaker. The Allies used them on the Eastern Theater, are basically guaranteed that the Japanese wouldn't be able to understand intercepted transmissions. So what you have now is great. Use the dragon soldiers as code speakers, speaking draconic. Logically, due to the fact that dragon have entirely different anatomy when it comes to speaking and hearing, the draconic language should be as incomprehensible to non-Draconic speakers as Navajo is.
About as effective as a human soldier
Which is to say, largely useless without training and technology, and fairly effective with. You've basically described a human who can (presumably) breathe fire. Human armies in WWII used flamethrowers as weapons, so that's not a radical change. Flame(thrower)s are very effective close-range weapons but useless at any great distance, so your dragons will still need to be competent users of long-range weaponry as well, just like human soldiers.
For my answer I will assume the dragon species in question has about the same level of intelligence as a very smart dog or dolphin, can breathe fire, and has wings which generate enough lift to carry its own body weight plus cargo (weight limited by the need to maintain flight). I will have to assume that these creatures are carnivorous, warm-blooded, and have a migratory lifestyle. Finally I will work with the assumption that the Allied and Axis powers field dragons at a rate similar to that of other war animals of the period, i.e. only for some very specialist uses.
I tried to go as stock as possible.
The firebreath could come in handy for razing urban areas, especially cities and towns with a lot of wooden architecture; after all the USAAF firebombed wooden-built Japanese cities to terrifying effect. However they will have to close in with their target, in contrast with most bombers which let loose their destructive payloads at a great height. In this sense dragons can be thought of as flesh-and-blood dive-bombers.
If they have a magnetic node which guides their migration (akin to many bird species), this could mean they will not face the same troubles of navigating inclement weather far from friendly bases as do the human-piloted aircraft of the era.
The most interesting concept to me would be if the dragons could use fire arms. By which I mean they rear up like a bear using their back legs and wings to balance themselves then using their forelimb to handle the weapon or weapons. Another thought that occurs to me is that even if we assume that the dragon’s body by itself is only as large as a human then there is going to be a lot of weight even with just the muscle for flight plus the wings. So dragons could probably handle larger firearms with their wings to help balance them and the added bulk, so that’s a possibility. My final thought is that dragons tend to have for intense and purposes “scales of iron” which sounds to me like the scales of a pangolin if you don’t know what that is look it you and then come back. For those of you who do here’s a little tidbit about pangolin scales, They are bulletproof. There have been reports of people getting injured but bullets ricocheting off of these creatures. Now given what I have read so far and the concepts I’ve put down I’m imagining a large bulletproof creature that can fly, rely secret messages, gather airborne intel, navigate better that most pilots, and hold back an entire platoon back by itself with nothing but it’s own napalm and heavy machine gun fire, all while despite not really wearing any armor takes a shotgun blast to the face while looking at you angrily. And to top it all off unlike your fellow man. It is showing no mercy to you or your soldiers. The thought sends both a excited and fearful shiver down my spine.