I think it has to be pretty high, something like 3.5 mmol/L, I think? I think the ketone meter goes up to 8.0 mmol/L before it reads HI. DKA isn’t JUST ketones but the ketones being so high that they affect the blood’s pH and electrolyte levels.
The highest ketone reading I’ve ever gotten is 1.2 after accidentally disconnecting from my pump for too long (a few hours!), and although I sort of freaked out, I don’t think I was in any real danger of DKA as long as I didn’t just ignore the number. Anything above 0.6 is “high” but not necessarily dangerous (just like a 200 mg/dl blood sugar is high and needs to be corrected, but isn’t immediately dangerous).
I have never been in DKA other than diagnosis 20 years ago, and have never thrown up from ketones (although a few times I came very close to the latter).