> What authority serves to provide transnational
> corporations their identity?
In "executive summary" terms: Lots of treaties and legislation in whatever may be the corporation-specific relevant country/countries at issue that are comparable in substance/function to U.S. state and federal corporate laws and, correlatively, lots of (within U.S. and non-U.S.) judicial and functionally equivalent rulings (e.g., for the most part, judicially enforceable arbitral and administrative agency decisions) within the U.S. and elsewhere rationalized for transnational enforcement purposes by way of the explicit contractual principles established thereby and also by imputed ones (e.g., most notably what are said to be principles of required "deference" or "comity") to achieve the basically Real Politick result that the courts and related agencies of countryA generally ought (i.e., rebuttably presumptively) give effect to what is enabled and required by the laws of countryB.
Granted, there has long been lots of putatively theoretical discussion and writing and teaching about this sort of Stuff ("comparative law" questions of what "authority" is there to recognizes "identity" of an organization referred to as a "corporation"? is a "corporation" just "nominal" or is it "real"? etc., etc) -- but, for the most part, posing this kind of query, as here, in abstract as distinguished from transactional/functional and otherwise fact--specific terms is a kind of "category mistake" famously criticized in a related but different context by Gilbert Ryle and other like thinkers (re. which, cf., the famous, ". . . but where's the university?" example).
> I used to think that Delaware was a
> 'flag nation' for corps.
Whether historically Delaware has been a favored state of incorporation within the U.S. (and also that this is somewhat less so these days) does not appear to have to do with anything else stated in this query.
> I guess my question originated when I was
> wondering what would happen to a corp if
> their articles of incorporation were vacated
> by the issuing authority.
Apart from avowedly being a speculative guess, this statement is a barely disguised tautology: What would happen if a corporation's charter were vacated by whatever is the state or country of incorporation would depend on what if anything else then happened in response to such revocation. Unless followed by some sort of remedial or other enforcement action, the revocation of a corporate charter (standing alone) might be an entirely moot act if, f'r'instnce, the (putatively no longer "existent") corporation's officer/directors/shareholders continue to act on the pretense that the corporation still "exists" and if no one else complains or sues.
IOW, its mostly an, "It depends . . ."[on the SPECIFIC relevant/operative FACTS]" sort of Thing -- again, on Real Politick -- far more than on abstractly "wondered" about general principles (though, certainly -- or, as the case may be, if an attempted real-life "case" were to eventuate, maybe not so certainly -- This or That asserted principle of law would be invoked to rationalize an argued for result).
> That would at least remove the fiction
> of their constitutional rights.
It is a "fiction" that corporations have constitutional rights only in the sense that any/every judicial ruling is a "fiction" as, correlatively, that corporations are accorded a variety of "personhood" related including many "constitutional rights" is a fact in every _functional_, i.e., PRACTICAL, way that matters.