Hmmmm. I'm getting the impression here that you're asking for help with something when you don't fully understand the question yourself.
What do I mean by this? Well, firstly you state that you want two flashing LEDs to be triggered by a micro switch. That part is fair enough. But then you go on to mention that you're not really concerned with how long they flash for, although you do throw 10 seconds up into the air. Personally I think you should know how long you want your own project to operate for! It doesn't have to be accurate of course; for example you could say: "I want the LEDs to flash for 10 seconds after the microswitch is pressed, +/- 2 seconds". That would be far more specific.
You then go on to mention that you're not too concerned about how the LEDs are to stop flashing. Either it can be via another switch (a reset switch) or the flashing LEDs can time out by themselves. Well... which one is it that you want?
My initial advice here is for you to have a sit down and think about your project, and decide how you would like it to operate. Then, when you've done that, have a think about how this might be accomplished. Post your ideas (even if it's just ideas in terms of discussion of methods) and then I'm certain you'll get positive responses.
Hope this helps,
Brian