Odds of Getting In
To get in, you're going to need to start as a copilot. On average, there are thirteen copilot slots in the entire United States air tanker fleet (source). Even if all thirteen opened up every year, that's not a lot of openings. Now realize that the aerial firefighting industry has an excruciatingly slow attrition pace, since pilots who enter the industry often don't leave for years. This trend results in pretty slim pickings.
We can, however, suggest a strategy that might help improve your odds: make yourself a superior candidate. Develop some additional technical or aviation skills, such as an Airframe and Power Plant Certification.
This will give you some real brownie points, as your employer knows you can legally fix problems with the aircraft you fly. Basically, anything you can do that will save them time and money will be one more reason for them to hire you above someone else.
Also consider working as a crop duster, which will provide you with near-to-ground flying experience. Since some firefighting aircraft are converted crop dusters, you'll have a slightly gentler learning curve. Working as a flight instructor will provide you with flight planning and quick-reaction skills, since you'll always be looking for a bailout strategy if your student does something incredibly unwise.
Finally, consider a stint as a ground-based firefighter, especially a wildland firefighter. Learning how the ground crews operate will help you better support them from the air.
Now that you've gained all these valuable skills, how can you use them to your advantage? Consider that most aerial firefighting companies forecast their staffing needs during downtimes, typically November through April.
In fact, they might even be stretching out on beach towels while sipping margaritas somewhere in the Caribbean in January. Get on their radar by sending your résumé, politely following up (without being too aggressive), and keeping the fire season timeline in mind.