The Paragon path for Favored Soul states, "... thus marking you as one of the heavenly host, kin to angels, and a special servant of your god." Does it turn the character into an angel?
Not really, no.
First and foremost, the text you are referring to is completely flavor. The only mechanical thing this grants is that the L16 property of this path gives you wings and a fly speed(provided you're in light armor). It also has a L12 utility that grants increases fly speed, so the flavor text does resemble the mechanics in that regard.
However, there is no change in origin, species or anything else listed in the mechanical portion of the text (the 2 L11 features, the L16 feature or the powers). The flavor text indicates the following (As you quoted):
Kin to angels does not make you an angel. More like a distant cousin of the species. You're still an elf (or a human or whatever race), you just resemble an angel now and have similar powers.
All that said, this is a flavor thing. If the right flavor for your PC is "I'm an Angel" and it's not intended to grant mechanical benefit, run it by your DM, this would be the kind of reflavoring that is encouraged in the books. (Just don't abuse it, this would be a narrative choice not a mechanical one)