Stronger legs (from cycling a lot/hills) translates into all areas of cycling. It will make hills seem flatter and flats seem slightly downhill. Hills suck, but they help a lot. Don't discriminate, ride all the hills you can find; big ones, small ones, long ones, short ones. Ride a lot of hills and maybe go up a gear to make it a little harder. That will build strength.

p.s. it's supposed to hurt

Generally, there is a benefit to all aspects of cycling to training on all aspects of cycling. You will see some benefit to your flat speed by training on hills, just like training for cadence, or training for sprints.

That said, it is not a sunstitute for training on flats. The vast majority of the benefits of hill training accrue to your ability to ride hills, while a small part accrues to your ability to ride flats. Likewise, the vast majority of speed training on the flats helps you ride flats faster, while some small part will help you on the hills.

The reason is that the technique and muscle recruitment is different for the two.

Consider that the power zone for hills is at a different arc on the pedal storke than for flats requiring the recruitment of slightly different muscle fibers. Think of it this way, going up a hill, you will need to use more strength to maintain a certain cadence. It is most efficient to use the additional power of your quads and less of the hamstrings. Therefore, most cyclists will tell you to concentrate on "kicking over the top" or "roll the log" which really means start your power stroke earlier.

In addition, the change in the angle of the road, effectively changes your center of gravity - which likewise changes the efficiency of your downstroke. Going up a hill, your weight is more behind your feet than on top of them. This will lead to a less powerful downstroke. You will usually find yourself compensating for this change with your upper body by "pulling" on the handlebars to generate more power. Incidentally, this usually means you are no longer in the aero position, but are riding on the bars.

By all means train on hills, but if you really want to improve your speed on the flats, do interval sprints in various gears on flats as well as on slight downhills. (The downhills really help train the neuromuscular ability to push bigger gears at high cadences.)

just like there is a difference between flats and hills, there is a difference between different grades of hills. But the real answer is this: variety in your workouts keeps you sane as well as improves performance. Mix it up.