@ddelphis: If you have an iPod or iPhone, you can download an app called Puffin. It's a browser that actually supports Flash ^^ The free version's Flash only works for two weeks though, but the app is only two dollars or so if I remember correctly.
It doesn't solve your computer problem, however...
@ChibiSilverWings: In a webcomic called "Homestuck" by Andrew Hussie, there's a lot of Flash games and such, and a few of the more recent ones were made with HTML5 rather than Flash, and they're actually pretty good ^^ There were character portraits, dialogue boxes, background music, and background images (and then a bunch of other stuff too). There wasn't a "next" arrow, but it would be easy to put in, I assume. In any case, I believe HTML5 can do everything you're doing in Flash now. :D
@MistPower101: Yeah, I'm sure we could accomplish much of our functionality in HTML5, however, none of use are programmers. stkbayfield has been learning basic Action Script to put together the comics as of now, and hopefully we'll learn more tricks as we go.
Coincidentally, I just started exploring the Ren'Py visual novel engine this week. That would be an ideal platform for this (and it requires no real programming skills to code.) Perfect for the interactive stuff too.
@HABE: I've worked with Ren'Py before (earlier this month, actually), and it is a wonderful engine. We're planning to do more with it later, but then we can't post it in small increments like we can on a website.