You could definitely recreate the game in HTML5 and use PhoneGap to package it for iOS. As long as you follow the app store guidelines, there's no reason why the game wouldn't be accepted by Apple.
The game logic seems straightforward enough and should, therefore, be relatively easy to translate to JavaScript. However, I think there may be significant effort involved in reproducing the animations you have, to an acceptable level of performance, using standards-based web technologies.
There are a few avenues I can think of which it might be worth your while exploring:
Google's swiffy will convert SWF files to HTML5 so you can use them on devices which don't support Flash. I have used it successfully to convert a reasonably complex Flash animation, however the performance of the animation on the device, when it was packaged as a native app for iOS using PhoneGap, was significantly worse than the Flash version. I'm not sure whether the tool would be capable of converting the whole game (definitely not if it's pulling in dynamic data), but you could certainly use it to translate the individual animations of the game.
Adobe Edge is an animation tool similar to Flash for creating animations in HTML. I've not used it so I don't know whether it's any good. However, it is still a relatively new product and a quick search for character animations using Adobe Edge wasn't particularly encouraging.
The CreateJS toolkit for Flash Professional is a free extension which will convert Flash animations to JavaScript using the open source CreateJS framework (which looks superb and may be a good starting point for rebuilding the game should you decide to convert it).
Convert the game logic from ActionScript 1 to ActionScript 3.0, reuse all your existing animations as is, and package the game for iOS using the Adobe AIR packager. Inevitably the performance won't be comparable to native, but I think it should be acceptable for this type of game.
I think in your case I would probably go for option 4, primarily because you'll save yourself the effort of recreating / converting existing animations in another technology. I would definitely encourage you to embrace HTML5 and associated technologies but would suggest you use them on a new project which will allow you to plan around its particular strengths and weaknesses.