If you want to heat up a wire, you'll need to know the rated ampacity of that wire. Since you don't care about the survival of the wire, and since you're actively trying to ignite something, you can then exceed that ampacity by several times. But that gives you a ballpark figure to start with.
Suppose we're talking about something relatively thin, 30 AWG. Three amps will heat that to about 90C, assuming typical ambients. Double the current, which quadruples the power, and you'll probably be at 250 or 300C. And that wire doesn't have much mass, so it should get to temperature very quickly. So to get it nice and hot, we need a source good for 7-10 amps.
You'll be lucky to get an amp out of a 9V battery.
I'd suggest using a capacitor. An electrolytic cap has (for your purposes) unlimited available short circuit current. All that will limit it is the resistance of the path and the energy in the cap. I'd probably do something like this:
simulate this circuit – Schematic created using CircuitLab
R1 limits the current from the battery to the cap, so there aren't any unpleasant sparks during wiring, and the battery doesn't see much of the current into the load wire. I'd probably use something on the order of 1 kOhm, 1/4W would be fine. Lower resistance means more power.
A 1-ohm R2 would give you about nine amps into your wire until the cap discharged. Discharge time will depend on the capacitance. Suppose you want that current for ten milliseconds, you'd probably want a time constant of 20 mS, so you'd need 20,000 uF of cap, probably rated for at least 12 VDC. That should be pretty easy to come by on Digikey.
These are all ballpark numbers, but it's an approach I would consider. Keeps your battery alive longer, avoids loading it past spec, and should be much more predictable and adjustable to get the results you want.