This is half-answer, half request to refine your question a little more, because it's not as easy to answer as you might think. I'll explain why.

We have various reconstructions of what we believe earlier languages are to have sounded like or been structured like, but since those are reconstructions and not attested languages, let's assume they fall outside the scope of your question.

That then brings up another issue. We have a good idea about what English sounded like in the Early Middle English period, but we again don't actually know. You're going to have seen videos on YouTube and sometimes posted on Reddit about "Shakespeare in the original pronunciation", but in fact this is not the original pronunciation. It's just someone's interpretation of the pronunciation. And if you see one of Shakespeare's plays put on in Original Pronunciation, you'll quickly notice that each actor has their own slightly different interpretation of it. The reason is because it is also a reconstruction, and there are holes in that particular reconstruction.

So then does that fit in the category of "known spoken language", and if it does, then do older reconstructions also? We have a very good idea of what Chinese of the Tang Dynasty sounded like, but we have no audio recordings. We also have a reasonable idea of what Proto-Indo-European sounded like, but again it's a reconstruction and we have no recordings. Where do you draw the line?

There is no specific point in time where we can say "this is no longer a reconstruction" unless we have clear documentation, and often that doesn't exist.

Taking a slightly different approach to the question then: Let's assume Proto-Indo-European (a reconstruction) counts. Let also assume Old Chinese (a reconstruction) counts. Which one is older? This is another question that gets asked fairly frequently. In the reply you've already received, the commenter makes a claim that a language is older than another. This is either completely untrue, or impossible to verify if it is true. It would be completely untrue if you believe that all languages share a common ancestor, because then every natural language (excluding creoles just to keep things tidy) would be exactly as old as every other natural language. Or it's completely unverifiable if you believe languages developed separately throughout human history, because we have no way of knowing when or how or where.

You can say that a certain proto-language like PIE might have developed in location X, but that doesn't actually mean it developed there. It just means that, in that reconstructed form, X is the most likely place where it was being spoken based on later migration patterns. However there would also have been a Proto-Proto-Indo-European which was the ancestor of Proto-Indo-European and something else, which was probably spoken somewhere other than X.

So when people say "[Language family] is so-and-so many years old" it doesn't actually mean that the language appeared one day, that many years ago. What it means is that a given point along the spectrum of constant continual development is being dated to that point. All languages are constantly in a state of change, so any dates that might be given are simply dates to mark a specific point in that change. As an analogy, if something changes from blue to yellow, at some point you might mark it and say "ok this is green at this point", but there's not anything really special about that point. It's just the point where your notion of green matches up.

This is why your question is very difficult if not impossible to answer, in the way that it's currently worded.

If in stead you ask "what is the oldest record of a language", then we can turn to the historical record and cite a particular stone tablet or bundle of bamboo strips. But it gets much much messier when we're just looking at spoken languages, especially since written records on the topic of spoken languages have historically been incredibly rare.

You could also try /r/linguistics as /u/caffarelli recommends, but a lot of us are on both subs, so asking here is probably also ok.

Try /r/linguistics!

It depends on where you draw the line of what a spoken language is (animals often have some spoken languages).

https://en.wikipedia.org/wiki/Talking_animal

But if you mean human languages, IIRC Noam Chomsky and others have done a bit of work dating known (and recorded extinct) languages insofar as mutations -- somewhat similar to that of https://en.wikipedia.org/wiki/Human_mitochondrial_molecular_clock

For example, Urgric Languages are at least twice or thrice as ancient as Indo European (almost all of Europe, including English), about 18,000 years old or more according to some reckonings. Basque is an isolate and much the same. Personally, I would like to see work done in New Guinea languages, as well as the Andaman Islanders.

Most ancient of all fairly pure languages are likely to be the Bushmen and Pygmies of Africa. Large mutations and conglomerations are normal for all languages in any time. It is believed that 'new' languages happen by a conglomeration of two or more different languages in times of distress or new conquests (e.g. moving into lands without habitation due to previous occupant devastation or virgin use).

Also possible is an important leader, especially during above said times, having a speech impediment or screw loose in the head. The rank and file would copy this. British lack of nasal use is said to be a recent invention, circa 1800's. Many spoke more like Americans before that. People copy those who are respected, and if a pirate colony ever took hold in say Namibia, Madagascar, or Australia, we might have had some interesting variations, maybe even our stereotypical accent:

http://dialectblog.com/2011/05/24/pirate-accent/

With this in mind we come back to the original idea of what is a language and how do we separate a language from a dialect. Usually it is if it is able to be understood by the speakers, with difficulty, or at least learned quickly. The same goes with species, the ability to mate with fertile offspring is not necessarily disqualifying to a separate entity.