Thanks very much. That is interesting indeed, as is the further FAQ linked in the wiki. My personal feeling is that Tolkien most likely did not create a backstory for the mysterious Bladorthin, but rather took this opportunity to use an interesting name that he had previoulsy devised for a different purpose but had discarded.

If I had to hazard a conclusion about the location of Bladorthin's kingdom, I would have to say either somewhere in the region of northern Rhun or else the portion of Rhovanion east of Southern Mirkwood and west of the Sea of Rhun. I would discount the area between the Misty Mountains and Northern Mirkwood as being too well documented in terms of its peoples (being the original homeland of the people that became the Rohirrim), and as being too lightly populated at the time of The Hobbit to suggest that during the height of Erebor's power that there might have been a kingdom there. On the other hand, I suppose it is certainly possible that there was then a small realm that fell to the orcs and of Gundabad (or the Misties more generally) for want of the spears that would have been delivered if Smaug had not intervened, and that the hardy woodmen of that region referenced in The Hobbit. are the survivors. In that case, we would have to think through whether it would be likely for the king of that realm to have an elvish name, and my brain is too tired right now to delve into that.

Interestingly the lotr.wiki for Rhun suggests that in addition to having been populated by Easterlings, Rhun was also the "peopled by lost Elves, Avari and Úmanyar, and by four of the seven clans of the Dwarves." I'm not sure where that information comes from, but if it can be trusted, given the apparent elvish etymology of the name Bladorthin perhaps we should conclude that he was the king of one of these elvish groups.

I haven't had a chance to look into who might have populated the portion of Rhovanion east of Southern Mirkwood and west of the Sea of Rhun at the time in question.