When Tolkien tells us that some of the Dwarves' rings were 'consumed by dragons' it could be taken one of two ways: they may have been eaten by the Dragons, or they may have been 'consumed' by Dragonfire as they were burnt up and destroyed. That second idea is very exciting!
Now, Dragons love treasure as much as Dwarves do, and the Rings brought to their bearers even more treasure - each was associated with a hoarde. Given that the Dwarves and the Dragons shared much of the North between them the chances of conflict must have been high. That some of the Dragons 'consumed' some of the Dwarves' rings must mean that there were independent Dragons, free of the control of Sauron and hence not terribly worried about destroying his Rings of Power in order to get their claws on that treasure (does this mean there were also female Dragons and Dragon babies?).
It conjours up all kinds of possibilities for truly Northern myths - tales of Dwarf Lords and their hoardes of treasure, glittering mountains of gold and gemstones hidden under the mountains; their power and wealth increased by the Rings they held, but their minds not fully corrupted. Then into the caverns came the Wyrms and the Drakes, some bold and brassy, some small and sneaky and concealing their literal firepower. There would be battles of course, and maybe at times stealth attacks, the clever Drake coming across the Dwarf Lord sitting proudly on guard outside the vault housing his hoarde and just blasting him to dust, having worked out that he needs to destroy the Ring in order to get hold of that hoarde.
And another thing that fascinates me...Why did Sauron want his Dwarf rings back?