As a firefighter and former woodstove user (and now a "Born Again Woodburner" as of Monday) I can tell you how some firefighters extinguish fires and you can make the call . . . "the call" being what you will do and how far you will choose to go.
As mentioned, the two most important things to do if you suspect you have a chimney fire . . . 1) Close down the stove as much as possible and 2) Call 911. The first step will choke the fire and the second step means professional help is on the way . . . as I often mention in classes . . . you may end up not needing the fire department, but it's always easier to get us on the way and then call us back and let us know you are all set and were able to extinguish the fire rather than not wanting to get us up out of bed/let the neighbors know you have a chimney fire/etc. and not call us until the fire is beginning to extend beyond the chimney.
Calling 911 early on is important . . . important if you live where I work in a City like Bangor . . . but really, really important when you live where I live in the country (Unity) since it takes us volunteers a little longer to get from our home to the fire station and then from the fire station to your home vs. going down the pole and driving to your home as a full-time firefighter.
Also worth mentioning . . . nearly every chimney fire I have been to has almost always been in a home where the homeowner failed to perform some routine inspection and cleaning of their chimneys. Checking your chimney once or twice a month is a good habit to get into . . . maybe even a bit more if your wood isn't completely seasoned. As a rule we encourage folks to sweep their chimneys if there is a 1/4 inch or more of creosote . . . but honestly, even then it isn't that big a deal to us . . . as I said, most chimney fires we go to are at the point where the chimney is nearly or totally blocked by creosote (on more than one occasion we need to use weighted chains to break through the creosote since it is so bad) -- we're talking folks that are very, very negligent in most cases rather than folks who failed to check their chimney two weeks before. Obviously there are exceptions, but as a rule it almost always seems to be that chimney fires are a result of bad habits . . . there is also another unwritten rule . . . all chimney fires usually occur at 1 a.m. in middle of a January blizzard with the temps around - 15 degrees and the wind howling at something like 20 mph . . . and the chimney can only be accessed by going up on a steep-metal roof.
In answer to your first question . . . any ABC-rated extinguisher is good. If you have a clean-out (such as can be found in a masonry chimney) open it up and give it a good blast. Usually the draft will carry the powder up and extinguish the fire.
An even simpler technique frequently practiced by us rural firefighters is to open the clean-out and if there is a bed of hot ashes/creosote to flick a bit of water on it (about a tablespoon or three). The water hits the hot ash/creosote and converts to steam. Steam expands and is drawn up the chimney. Honestly, this works in 9 out of 10 times we try it . . . the key is to not dump massive amounts of water into the chimney as steam expands a lot and too much too quickly can result in a ruined chimney. I've never tried the wet newspaper idea, but have heard of folks using that idea as well.
If you're on the roof you can also drop or sprinkle baking soda (we often use powder from old fire extinguishers in baggies -- we call them chimney bombs) down the chimney.
I have also heard of folks using flares or similar devices to extinguish the fire in the woodstove . . . not sure how well they work though.
If things are really bad (and when we are called they often are) we end up going to the roof and breaking through the creosote when a weighted chain and then sweeping it with a brush.
Shut the stove DOWN ASAP! Cut off all intake to it and let it go out. If the freight train doesn't stop CALL the fire dept. It's better than losing your house.
