I'm not sure if you're dripping or dipping, so if my advice is off as a result, my apologies in advance!
If you're dipping, I've never done that, so haven't got much experience, but my understanding is that dipping grabs just the right amount of liquid automatically, so should be problem-free as far as flooding is concerned. If you're dipping, then it's possible you've flooded the atomizer by dripping too much
juice onto it. How much did you drip? I drip two or three drops onto a 510 atomizer. Any more than that and it will gurgle, be hard to vape, not have much flavor, and produce hardly any vapor.
If you've flooded the atomizer, you can disconnect it from the battery and cartridge or drip tip and blow through it while holding it over a paper towel to get all the excess liquid out of it. Some people recommend only blowing through the threaded end (the end that connects to the battery). Others recommend blowing through both ends. I'm a both ends kind of girl, but your mileage may vary.
It's also possible that you need to adjust the way you're dragging on the e-cig. Here are a couple of links that might help if that's the problem:
[youtube]0U8EckqYyC8&[/youtube]
[youtube]GFg_7vKWkfw&[/youtube]
It looks like a couple of people have already replied as I was writing this, and I agree with Upinthehills about the primer puff. I do the same thing. I take a quick puff and then follow it with a long drag. I don't know why this is better, but it just is.
When you say the caromizers have burnt out, do you mean they're no longer functioning at all or they're out of fluid? If they're out of fluid, you should be able to refill them and continue using them.