On a recent trip, I found that the TSA did check my checked luggage,
and removed safety matches from my stove bag as well as the spare
matches in my first aid kit. They were wooden matches, but safety
matches (not strike anywhere) but apparently the inspector thought
they were not permitted. Imagine my surprise at my first campsite
looking for my matches.
No problem with the stove or fuel bottle, but I did wash the fuel bottle
with soap and water before packing it.
--------------
Here is what the TSA says on their web site...
Lighters ALL lighters are banned from your carry-on luggage.
Lighters that do not contain fuel are permitted in checked baggage,
but lighters with fuel are not.
Matches Matches are not permitted in your checked baggage, but you
may carry up to four books of safety matches in your carry-on baggage
or on your person. Strike anywhere matches are prohibited at all times
from carry-on and checked baggage.
Camp Stoves You may pack your camp stove as carry-on or in
checked luggage ONLY if it is empty of all fuel and cleaned so that
there is NO smell of fuel. Simply emptying the fuel container is not
sufficient.
-----------
A PDF of prohibited items is at
http://www.tsa.gov/public/interapp/editorial/editorial_1012.xml