On Medium and littler half-dragons and pre-existing wings
The template half-dragon in its Speed entry says
A half-dragon that is Large or larger has wings and can fly at twice its base land speed (maximum 120 ft.) with average maneuverability. A half-dragon that is Medium or smaller does not have wings. (Monster Manual 146)
At this point in the game's lifecycle, it's totally legit to parse that second sentence as deleting a Medium or littler half-dragon creature's wings. I mean, it's not as if someone can deny that the words say A half-dragon that is Medium or smaller does not have wings. It really says that, and that statement in isolation can be taken as an absolute, incontrovertible fact. Is it a Medium or smaller half-dragon creature? Then it ain't got wings because a half-dragon that is Medium or littler just does not have wings. Done.
However, that statement can also be read in context. That is, while it's totally valid to read that original statement to mean that A half-dragon that is Medium or smaller loses any wings therefore probably any fly speed it may have, I've always preferred to read that as A half-dragon that is Medium or smaller does not have wings from this template yet keeps wings gained from other sources.
I've no published examples of creatures supporting either position, though. So far as I'm aware, Wizards of the Coast never applied the half-dragon template to a Medium or littler creature that possesses a fly speed. In fact, there aren't nearly as many half-dragon creatures as I originally thought. For instance, apparently no half-dragon creatures were published in Dungeon or in Dragon, and besides the Monster Manual's fighter (146–7) and lammasu (165–6) and Frostburn's rhemoraz (196), there's just the half-dragon creatures from the Draconomicon Web enhancement "Half-Dragons: Twice as Much Fun." Neither the basilisk nor the medusa could fly originally and still can't post-template, and all the other half-dragon creatures therein are Large or bigger. So, yeah, I don't think we can know if A half-dragon that is Medium or smaller does not have wings is supposed to be a standalone fact or a context-dependent statement about the template. (I didn't check every every source for half-dragon creatures. I apologize if I've overlooked your favorite half-dragon creature, and please comment if an overlooked half-dragon creature is relevant to this answer!)
Still, I can justify my decision to allow half-dragon creatures to keep their existing wings. Even if a DM ignores the sledgehammer that is CR, a DM who's trying to make a challenge more difficult for the PCs will find the half-dragon template lacking if it also deletes a naturally flying Medium-or-littler creature's wings. I mean, I'd expect that applying the half-dragon creature template to a hawk would make it more dangerous than applying the template to a cat, but the opposite is true: The wingless half-dragon hawk hopping around at its 10 ft. land speed is just kind of sad, but the fire-breathing cat is terrifying.
So, really, unless there's a compelling reason to want to use the template to delete a Medium-or-littler creature's wings, this DM recommends not having the template delete a Medium-or-littler half-dragon creature's existing wings. Let, for example, that half-white dragon owl (273) or that half-copper dragon grig (235) keep its original wings.
On Large or bigger half-dragons and pre-existing flight speeds and maneuverability ratings
Given the dearth of half-dragon creatures, the approach taken by the Draconomicon Web enhancement "Half-Dragons: Twice as Much Fun" seems reasonable enough: when the half-dragon template is applied to a creature that can already fly, the higher fly speed is kept. Further, it seems that if the creature's maneuverability is poor, it becomes average. Still, there are only three useful examples.
- Tibulliax, a half-copper dragon androsphix (1—2) and its 100 ft. (average) fly speed. (Instead of the 80 ft. (poor) fly speed of the typical androspinx, it has a fly speed of twice its land speed and average maneuverability as per the half-dragon template.)
- Azuria, a half-silver dragon djinni (2–3) and its 60 ft. (perfect) fly speed. (It has a normal djinni's fly speed instead of the 40 ft. (average) fly speed that the half-dragon template would grant.)
- Scythia, a half-brass dragon wyvern (6—7) and its 60 ft. (average) fly speed. (It has this instead of the 60 ft. (poor) fly speed of the typical wyvern or the 40 ft. (average) fly speed that the half-dragon template would grant.) This is the only evidence I could find for improving or changing maneuverability due to the presence of the half-dragon template.
(Full Disclosure: Kalivia, a half-blue dragon yuan-ti abomination (7—8) completely lacks a fly speed despite being size Large. Thus, because this WE has other errors, that may cast a pall upon any argument for improved maneuverability using Scythia as an example. I'm sorry.)
Anyway, using these as examples, a half-silver dragon solar (MM 12–13) should keep its 150 ft. (good) fly speed from its angel wings rather than seeing that substantial and awesome fly speed be replaced by the woeful 100 ft. (average) fly speed from its dragon wings.
Alternatively, I can imagine a DM bypassing the examples completely, recording both fly speeds, and adding dragon wings to every Large or bigger half-dragon creature even if that means two or more pairs of mismatched wings. I doubt that would in any way hurt game balance, but it might hurt the eyes and/or brain.