Or not. Flat earthers are quacks.
It is the same principle essentially. It is illogical to think "hey if I keep walking that way I'll hit a wall eventually". That is why flat earthers are quacks from the beginning.
The same principle applies to space. What quack seriously thinks that eventually there is just a wall in space or that it wraps around?
Wrapping around makes zero sense in 3-dimensional space.
...if the universe was like a "3-torus", it could be both flat and finite: https://en.wikipedia.org/wiki/Three-torus
If you ever played the classic game "asteroids", you might remember how everything wrapped around at the edges of the screen. A 3-torus would be like that, only in 3D.
On the other hand, one could imagine the universe as a 3-sphere, which I believe would mean it would be both locally curved and finite in volume. https://en.wikipedia.org/wiki/3-sphere
There are also other possibilities, like something analogous to a Klein bottle with an extra dimension.
There are a bunch of possibilities for "flat and finite" as well as "positively curved and finite" that I can't begin to visualize.
There is even supposedly such a (hypothetical) thing as a negatively curved, (commonly described as saddle shaped) yet finite universe.
But regardless, the current belief about the real universe is that it is at least very close to flat, but not known to be finite or infinite.