This is right up my alley..... But, i've always been a big advocate of "the custom is always right" FOR THE MOST PART. First, just ask your pool builder to see what they can do. Explain that it bothers you, and you would like it to look like it was originally installed. A good swimming pool company will usually address ALL of your concerns, no matter how trivial.
Now here's the challenge. Flagstone is a soft stone, so, it's going to scratch & degrade over time. In fact, i've seen some flagstone copings literally FLAKE away in layers... Flagstone is made of lots of small layers of sand, compressed together over time. It's actually pretty easy to buff out, but it then creates a more noticeable area that is smoother than the other stone. So, in my opinion - it's better to leave it, and let it buff naturally as you use the pool. It doesn't seem like replacement is warranted, but that's the worst case scenario (and they won't like you for that.....but, you are the customer) Most pool companies are NOT stone experts, so make sure these guys test a small area if they offer to fix it. Make sure you like the fix before they do all the scratches. Once buffed, there is no going back!
While I'm thinking of it, make sure you DON'T have a salt system! Salt and Flagstone don't mix. The salt crystals are 4 to 5 X larger in dry state, than in liquid. So, these guys get into the flagstone very easily, dry out, expand, and will actually turn the flagstone to DUST over only a few years. we've been semi-succesful with sealants, but sealants wear down.