In all the reading I have done about Tolkien I have never read anything about dual citizenship. So I would say no. I will let some of the others weigh in on this also.
And would be horrified to be considered anything else. He identified strongly with the West-midlands and the ancient Mercian tongue ("I am a West-midlander by blood (and took to early west-midland Middle English as a known tongue as soon as I set eyes on it)" [Letter #163], and was enamoured of his Anglo-Saxon roots via his Suffield heritage.
He considered himself English, as opposed to British. And although he did travel extensively on the Continent and Ireland, he never ventured elsewhere, and never took a dual citizenship - unless, of course, you consider him to also be a citizen of Middle-earth! []
Just teasing. Is there a specific reason you might have thought he had dual-citizenship? He was born in South Africa, but I don't know for a fact that he had (or didn't have) any other legal citizenship than England.
on Wikipedia, I get the impression that people born in South Africa before 1949 were simply British subjects. After 1949, Tolkien might have been eligible to claim South African citizenship if he'd wanted to, but there would have been no reason for him to want to do so since he'd left as such a small child and seemed to have no further links with the country. (One complication is that back in the days of the British Empire, citizenship wasn't thought of as a right - instead, you were a subject, which was seen as a duty. You owed allegiance to the King or Queen of the day. You couldn't choose to give it up, and as far as I know it didn't give you any particular rights to live in another country in the Empire.)
when Tolkien was born there was no such nation as South Africa (founded 1910). His parents, while residents of the Orange Free State (then an independent republic), were British subjects and therefore so was he.
I'd always just assumed that JRRT was born in "South Africa", rather than in a location that subsequently became part of South Africa. And I'm afraid I'm woefully ignorant about the history of the Boers and all the rest of this period in Southern African politics.
[Tolkien's] parents, while residents of the Orange Free State (then an independent republic), were British subjects and therefore so was he.
Tolkien would clearly have inherited his British status from his parents (as would still be the case today), but unless the Orange Free State had different rules than most modern countries, he would also have been entitled to citizenship of the State, by virtue of having been born there. So, whether he ever claimed it or not, it seems quite possible that he would have been entitled to dual citizenship. By analogy with one somewhat similar example I happen to be more familiar with (Newfoundland which became a part of Canada in 1949), I would have expected that anyone born in the territory which subsequently became part of South Africa would be entitled to South African citizenship.