Not a word that you should use to describe yourself - but are you? Are you complacent? Flash has had a good run - and while it's true that Flash isn't going away anytime soon - it still has it's uses. But for online content - especially banners and intro pages for websites, video is going to take hold like never before. I expect that because a few of the main carriers for mobile phones will be switching to 4G and because broadband saturation will be reaching untold numbers, this will free content in a way that has never been possible. Imagine producing a online media campaign that would rival in looks that a major motion picture has in effects. What this means for you is that you need to build up your skill-base and get to a point that you can compete and excel.
Now you may say that you think Flash is still usable and that there's no reason to learn a new program or go deeper into the programs that you know; but honestly if you don't start to learn some of the basics of Video Editing and Motion Graphics you might very well find that you'll be left choking on the dust of those who do know After Effects, Premier, Final Cut etc.
If you're satisfied just doing what is necessary to get by and you feel that your knowledge of Photoshop and Flash can get you by - then by all means just keep on doing what you do. Don't be surprised though if you aren't promoted, you aren't chosen for juicy projects, and you constantly are just doing "grunt" work. You might start wondering why the new guy who just got hired 3 months ago got a promotion above you and seems to be involved in several initiatives. The answer is simple - they know programs that you don't and are able to produce more engaging content because of it. It's fine to concept - but if you can't execute and do not know what is possible then how can you compete?
If you want to be involved in the latest innovations and the best creative then I suggest you take heed and start to actively learn the tools you will need to go further in the web/internet/mobile space. A good start would be AfterEffects - this is probably the most widely used Motion Graphics and Compositing tool out there. Not only that but starting now and using it even for minor personal projects will let you get a good foothold on how you can incorporate it into your process. For editing video: Premiere and Final Cut are the two programs that will help you get to where you need to be. Video editing isn't any harder than creating a complex Flash piece and because you understand the fundamentals of animation using After Effects and an editing program probably will not be that hard and you could start doing it today.
Aside from learning new programs (new to you anyway), there is one program you use probably everyday that will increase your capabilities across the board, Photoshop. Photoshop isn't just for static images - you can create motion graphic pieces, re-size videos, bring in 3D elements, edit video and more. There are so many tutorials on this and Adobe has published several videos, online learning tools etc., that the mere fact some designers weren't aware of it - makes me sick.
Why not experiment and get going on this tried and true program that has had these capabilities since CS3. What? You didn't know? My question for you is - why not? How come you didn't know? Were you asleep for 3 years?
I'm not saying that Flash should be abandoned alltogether - but that as a new media designer you should take a step forward and integrate some of the possibilities of using video WITH interactivity.
If you need advice or tutorials the internet is swamped with literally thousands of tutorials - Vimeo and YouTube and good places to start, but almost any search engine will produce hundreds of website locations with tutorials and downloads that will keep you in the know (most of them are for free). Beyond that - my suggestion is much like Nike's motto - just do it.
Here's a few sites to get you started in learning motion graphics, video editing and compositing: