Of course they did. That's the only way to make sense of the plethora of fossils showing various birds throughout geological history. The fact that they arose by evolution makes a heck of a lot more sense than a belief that they popped into existence fully formed.
Tell me this and I might at least listen:
You're claiming that creatures which had down feathers for insulation evolved into flying birds (including eagles). Flight feathers however resemble down feathers in no way, shape, or manner. A flight feather has interlocking barblets and hooks for structural strength (to hold the bird up in the air) which a down feather doesn't begin to have. If flight feathers evolved via any sort of mutation, then ALL of the creatures feathers would change into flight feathers since the creature had down feathers all over his body. Nonetheless the flight feathers only exist in the precise areas in which the eagle needs them, i.e. his wings.
How did flight feathers evolve only where the flying bird needs them? Why doesn't the eagle have flight feathers all over his whole body??
Look here for a drawing of various evolutionary stages of feathers.
Keep in mind that structures don't suddenly appear in the complex forms with which we are familiar. They appear in simple forms and gradually become more complex. The only requirement for that process is that the change is not deleterious; that it is neutral or advantageous for survival.
Another thing to keep in mind is that there is no evolutionary principle that precludes structures on different parts of the body having different appearances. If you would hypothesize, for instance, that a mutation in a flight feather would also appear in every other feather, you have to explain why you made that hypothesis, and support your explanation with a discussion of the genetics you think are involved. A mutation that affects feather development might not be in a feather gene--it could be in a gene that you don't even think is involved in feather development. I should also point out that there is no reason to think that feathers had either a flight or insulation function when they first appeared. Since they were probably modified scales, a likely function of early feathers would have been for protection (like the scales).
One more thing, and that is that you seem to think a feather is incredibly complicated. It isn't, really. If you look close, you will see that it is essentially one basic structure repeated dozens of times on each side of the central support, in a fractal pattern. Fractals and repetition are extremely common developmental themes. You see that kind of repetition in your limbs (longer bones of the arm > shorter bones of the hand > three progressively shorter bones of the fingers), your ribs, the rings of earthworms, scales of fish, plant leaves, etc. That repetition means that the structures actually aren't as complex as you might think.
As for why the eagle doesn't have flight feathers all over its body--well, that's because it doesn't have wing-differentiated cells all over its body.
All I saw there was BS. Flight feathers on arms which weren't wings yet would serve zero purpose other than getting torn off or damaged as the creature tried to use its arms for grasping or whatever, leaving the creature colder than when he had down feathers in the first place. Natural selection itself would mitigate against it.