Well. Since ODG patiently asked (several times) and Stilt namedropped me..
Flash is connected to everything and everyone through the Speed Force, as it touches every part of reality:
OK. So he doesn't need to be in physical contact to affect someone's speed. Let's look at examples of this.
Let's start small/tangential. He can lend speed without touching them:
https://i.postimg.cc/fbpqXDMW/A2.jpg
https://i.postimg.cc/HLR5sN3y/21.jpg
O...K? That's lending, not stealing.
H1 has already posted an example. Here he is against bullets:
OK. Not living beings. Let's go higher.
OK. A bit better. But Girder isn't a speedster, that was close proximity, it was only a few moments etc etc etc (yes, I am assuming people will try to move the goalposts).
That's a speedster. But it's a 2d representation of a 3d event, so mayyybe he....groped her as he went past? But at least she's better than Girder, amirite? And it lasts a good while (bonus for abhi who I think said he's only ever done this longterm speedsteal against Inertia).
But nobody knows who Lady Flash is. Here he is, taking the kinetic energy from Superman and WW:
https://i.postimg.cc/zfMrtsF3/22.jpg
Then there is the Human Race storyline, where he takes speed from everyone on Earth, including Superman (note that WW isn't even mentioned as one of the fastest beings on the planet):
Not as clear-cut as the others, as the Cosmic Gamblers had created a link through which information could be transmitted instantaneously (hence him being able to chat to Linda across the universe).
In short, once we aggregate the various scans, yes he can speedsteal from non-speedsters, yes he can speedsteal from Supes, yes he can speedsteal/speed lend without physically touching them.
Am sure there are more examples, those are just the usual ones that popped into my head.