The short answer is "he very well might lose his power". The longer answer requires understanding how DC structures their comic book stories, so buckle up.
The terminology is a bit confusing here, because Marvel and DC don't have "universes", they have "multi-verses". Since you're specifically asking about "in another universe", it's important to make that distinction.
The "DC Universe" is not one universe. It's actually a multi-verse, consisting of many different universe with their own separate histories, characters, etc. The Flash from one DC universe (e.g. "Earth One" or "New Earth", depending on what year is it) can travel to a different DC universe within the Multiverse with no problem. In fact, Flash is somewhat unique in this regard, as the Speed Force is often cited as the key element of the multiverse that ties such things together. Thus, if you're using universe in the sense of "the entirety of space and time in a particular physical reality", then Flash can go to all kinds of universes, and be just fine.
However, DC also has the concept of multiple multiverses, which is usually called "The omniverse". The Marvel multiverse exists within this omniverse, and on very rare occasions, DC characters can go there as well. However, there's some things to keep in mind here:
- Marvel's multiverse consists of a lot of universes, each with their own rules. You can't necessarily apply what happens in one universe to the others.
- The Marvel multiverse is now officially "part of" the DC omniverse. By definition, anywhere a DC character ends up becomes part of the DC omniverse. Thus, in the sense that the average person uses the word "universe" to mean "everything that could ever possibly exist", it's not really correct to say that Flash can ever be outside of the DC universe.
- Most Importantly, these crossovers are almost always non-canon -- as far as the primary history of DC's characters is concerned, they never happened. Thus, you have to be very careful not to make any generalization about them; the next author to do a Marvel/DC crossover could very well ignore any previous crossover stories, and make up her own rules.
Having said all that, one of the most popular DC/Marvel crossover events was the "Avengers/JLA" crossover from 2003. In that series, the JLA from DC's main New Earth were pitted against the Avengers from Marvel's main Earth-616 as part of a pan-multiverse game between two really powerful entities.
Flash was able to travel to Earth-616 in person, but once there he found that there was no Speed Force, and so he lost his powers. Eventually he is pulled back into his universe. Quicksilver, on the other hand, has no problem using his super-speed on New Earth -- though he does lose the fight w/ The Flash in that setup.
So, yes, it is true that in at least one case where The Flash found himself in a universe that is not part of DC's usual multiverse, there was no Speed Force and he lost his powers.