In Pathfinder, the Web spell explicitly has this to say about flammability:
The strands of a web spell are flammable. A flaming weapon can slash them away as easily as a hand brushes away cobwebs. Any fire can set the webs alight and burn away one 5-foot square in 1 round. All creatures within flaming webs take 2d4 points of fire damage from the flames.
The Web (Ex) ability, on the other hand does not say anything about fire at all:
Web (Ex) Creatures with the web ability can use webs to support themselves and up to one additional creature of the same size. In addition, such creatures can throw a web up to eight times per day. This is similar to an attack with a net but has a maximum range of 50 feet, with a range increment of 10 feet, and is effective against targets up to one size category larger than the web spinner. An entangled creature can escape with a successful Escape Artist check or burst the web with a Strength check. Both are standard actions with a DC equal to 10 + 1/2 the creature's HD + the creature's Con modifier. Attempts to burst a web by those caught in it take a –4 penalty.
Web spinners can create sheets of sticky webbing up to three times their size. They usually position these sheets to snare flying creatures but can also try to trap prey on the ground. Approaching creatures must succeed on a DC 20 Perception check to notice a web; otherwise they stumble into it and become trapped as though by a successful web attack. Attempts to escape or burst the webbing gain a +5 bonus if the trapped creature has something to walk on or grab while pulling free. Each 5-foot-square section of web has a number of hit points equal to the Hit Dice of the creature that created it and DR 5/—. A creature can move across its own web at its climb speed and can pinpoint the location of any creature touching its web.
Can you burn through a conventional spider web if trapped in it, instead of the Escape Artist/Strength check?