Are there any dragons in any mythological canons that have been able to breathe fire while underwater?
There isn't a much detailed information on dragons until the modern period, due to the sparser descriptions in ancient mythological canons vs. highly descriptive modern forms like the novel.
The first definitive mythological record fire-breathing dragon may come from Beowulf, and the idea definitely got traction in Western folklore. (By contrast, Chinese Dragons are associated with water, can take the form of fish, and are often tasked with bringing rain. The famous Hindu dragon, Vritra, is associated with drought, being a blocker of rivers. Tiamat, sometimes depicted as a dragon, was the goddess of the salt sea.)
In modern fiction, dragons have all kinds of powers, and I wouldn't be surprised if there are examples that can breathe fire underwater. But for the purist, it might be worth looking at Tolkien, who was a respected scholar, and may be said to have commented on the subject in the form of Smaug.
In "Fire and Water", the 14th Chapter of The Hobbit, it is said of Smaug that:
[Smaug's] enemies were on an island in deep water-too deep and dark and cool for his liking. If he plunged into it, a vapour and a steam would arise enough to cover all the land with a mist for days; but the lake was mightier than he, it would quench him before he could pass through.
SOURCE: The Hobbit (1937)
It is strongly implied that to be quenched by the lake would be death to Smaug, based on the elemental nature of such powerful entities in Tolkien. The description of Smaug's death, albeit by a black arrow to the heart, reinforces the power of water over fire:
Full on the town he fell. His last throes splintered it to sparks and gledes. The lake roared in. A vast steam leaped up, white in the sudden dark under the moon. There was a hiss, a gushing whirl, and then silence. And that was the end of Smaug and Esgaroth...
The is a solid basis for Tolkien's choice in that water is generally, and alchemically, to conquer fire--rains quench wildfires, oceanic magma is "turned to stone" by contact with water.
The Chinese Wu Xing is particularly instructive in this regard. In the linked image you will note that fire "insults" water, and that water "destroys" fire.
Traditionally these two elements are mutually exclusive.