Focusing on one skill will limit your career prospects. You should become knowledgeable in as many aspects of modern Flash implementations as possible if you want to continue in a Flash-related career. AS3 will likely follow the footsteps of AS1/AS2. Staying on the learning curve is a necessity for a programming career, especially if you seek to be employed and not self-employed.
I guess a lot depends on where you are looking for work. you can certianly continue purely with AS3 but you options would be more limited.
I haven't seen that much demand for Flex, it's certainly a small percentage of the jobs I have seen.
As for mobile this is big area for AS developers at the moment and knowing some wouldn't hurt.
If you want to move and give yourself as much chance as possible I would suggest trying to build demos in a variety of application platforms.
Create a simple mobile app, do some social networking (e.g. a facebook game) and possibly a smiple Flex application and apply for these jobs. 3D demos can really impress as well. you might not have the commercial experience but if you have the demos, come accross well, demonstrating you want to learn these technologies and you know the basics you have a good chance; depending on who else applies.
A good company will realise you have a good grounding in AS and can apply what you know to these new areas. For a good developer moving from web based AS to mobile is not hard a every company should know this. There is a little more to learn for Flex but if you have the time is well spent, however someone looking for a Flex developer might be a little more demanding in terms experience
as a side note I got my first AS3 gig with no flash experience at all. I came from a Java background and a good relationship with Sega and developed the original sonic engine for their playSega website
Thank you Ned Murphy. As you said focusing on one skill will definetly limit my career. I just want to improve myself by learning and practicing each and every implementation coming in flash technology and also want to concentrate on mobile applications.
Thank you so much _spoboyle. I think you guided me in a right way. Mobile apps having so much of demand today. Having knowledge in mobile apps is good for my career. I want to update myself with new technologies coming in flash. And also want to learn basics in flex and making 3D games.