I’m pretty much agreeing with Dmitriy Genzel’s answer: Dmitriy Genzel’s answer to How long would it take for English from anglophone countries to become separate languages?.
If you look at my related answer to How long would it take an isolated group of people to develop what would be considered their own language?, you’ll see that historically, it could take something like 500 or 1000 years for languages to diverge. Universal literacy has a profoundly conservative effect on language, however, and those effects look to be intensifying, as English-speakers from different parts of the world are now becoming more in contact, not less.
This does not mean that their dialects are actually converging. Linguists have argued that vowels are currently off doing their own thing in different parts of the US, and there is no evidence that the subdialects of US English are converging—the opposite is happening. There are several clear grammatical differences that are entrenched between different variants of US or British English.
But my guess is that there are enough conservative forces in the current Anglophone culture, to slow down any divergence of national variants English significantly, compared to the historical norm.
Whether those conservative forces remain in place—that is to say, whether Western Civilisation or Globalisation survives—is an entirely different question.