It was never revealed as to how old she is, but we can theorize a bit via other mediums where she appeared in
We can always take some hint from the manga. Ruby (Brendan's manga counterpart), fought her Salamence when he was very young when she went on a mission to free Rayquaza from the capture of the humans so that they could create an Orb to control it, like the Ruby and Sapphire is there for Groudon and Kyogre respectively, which ended up with her Salamence striking down on his head and leaving behind a scar, which happened 6 years prior to the Ruby and Sapphire manga and 9 years prior to the ORAS manga. Ruby in ORAS was somewhere around 15 years old, so 9 years prior to that would be when Ruby was around 6 years old. So for Zinnia to have a Salamence and actually fight with young Ruby and go on such a dangerous mission back then, she has had to be in her own early teen years, at the very least. So nine years after that, I'm assuming she would be around 21 years old.
Now, I know that the games are different from the manga, but a lot of things are quite similar too, especially when the manga and game events are very similar. Also that Aster, well, in the manga, she was one of the Draconid people, someone with a very special ability. When she died, the Draconid people had to choose someone to be her successor, and that's when Zinnia stepped up to be the candidate for it. So there was no direct connection between Zinnia and the original Aster, and definitely Aster was not her daughter.
And the games shouldn't be far from this lore too, it would be very awkward. Though, seeing the manga and comparing it with the games, she has to be in her late teenager years or in her early adult years, around 20 , most probably.
