No. It specifies three spells and other similar fire spells that can burn away the mist, but non-magical flame isn't mentioned. Since magical and non-magical winds are mentioned, the lack of mention of non-magical flames is conspicuous and strongly implies that the flame must be magical.
From a common-sense perspective this makes sense. It wouldn't be much of an obscuring mist if something as easy as waving a torch around could disperse it, right?
Looking deep into the spell
The spell states that it is an illusion (figment) [fear, shadow] spell, meaning that it has two parts the [fear] and the [shadow]. The spell goes on to describe that the shadow part has a quality that obscures vision and provides concealment, that much is understood. The fear portion of the spell is the "Illusion of misty vapor inhabited by shadowy shapes that arises around you". The (figment) tells us this "A figment spell creates a false sensation. Those who perceive the figment perceive the same thing, not their own slightly different versions of the figment. It is not a personalized mental impression." This tells us that the spell does not change, and that the shadowy images and shapes that dwell within the mist do not change or get worse, they are the same for everyone.
This means that the spell is not doing physical harm to your body, but instead the images are scaring you mentally (The wisdom damage). It is not a gaseous vapor that you are inhaling every 6 seconds, it is a shadowy illusion spell that has a specific impression meant to mentally scar you. You are either fooled by it or you are not. You don't simply believe that the shadowy shapes and misty vapor is indeed a spell fooling you one second, and six seconds later completely believe they are real. Cloudkill requires a save every round because you are still subjecting your body to the poisons, the illusions on the other hand are figments, they do not physically harm your body.
Fear effects are compounding.
The bottom of the spell description states that "All creatures within the mist must save or take 1d2 points of Wisdom damage and gain the shaken condition." Under the fear description (page 563 cr) it states "In most cases, the character makes a Will saving throw to resist this effect, and a failed roll means that the character is shaken, frightened, or panicked.", it goes on to say that "Fear effects are cumulative, a shaken character who is made shaken again becomes more frightened, and a shaken character who is made frightened becomes panicked." This addresses the "shaken" part of the fear spell.
Final Conclusion
A creature would only make a save. If they fail their save, they are mentally scared and take 1-2 points of wisdom damage on top of being shaken for as long as they remain in the mist. Leaving the mist after failing a save would mean that the character still keeps the wisdom damage, but loses the shaken effect. Should they re-enter it, they would inherit their last fear effect (Shaken, Frightened, Panicked). Fear effects are disbelief based, which means that the second a character makes a successful Will save, they no longer have to make another save, they already know that the spell is just an illusion.
However
It does state that fear spell are compounding, and fear effects go from Shaken to Frightened, Frightened to Panicked. As a DM you could have players make multiple saves should they fail their first one to determine if the level of fear increases, but that is part of the spell is only in place should they already have the shaken condition. The Figment part of the spell suggests that because the spell does not change, the player would not take consecutive wisdom damage, the damage is already dealt upon seeing the shadowy shapes. It is up to you as a DM to decide the final ruling.
Best Answer
This DM is inclined to rule that a creature suffers no miss chance when attacking a foe 5 ft. away that's under the effect of faerie fire yet that's within the effect of an obscuring mist
The effect of the 1st-level Sor/Wiz spell obscuring mist [conj] (PH 258) is an effect similar to those listed in the description of the 1st-level Drd spell faerie fire (PH 229), which includes both mundane and magical effects.
Initially, I leaned toward saying the miss chance should apply, given that the spell obscuring mist is a conjuration (creation) school spell, but the spell faerie fire overcomes (completely mundane) darkness and (possibly mundane or, at least, not italicized) displacement and invisibility, likely putting the misty vapors conjured by the spell obscuring mist in the same boat as those. (The majority reach a similar conclusion in this 2012 Giant in the Playground forum thread.)
If this were a serious issue in my campaign, I might go so far as to rule that in this case darkness and fog are approximately equivalent, so that the spell faerie fire reveals clearly affected creatures within a not-so-dense fog (like the Interesting Combat factor fog on DMG 17) and affected creatures within 5 ft. of the viewer within normal fog (DMG 94) and a 1st-level fog effect like that created by the spell obscuring mist. But I'd also rule that faerie fire's blocked by the fog effect a higher level spell (e.g. the 2nd-level Sor/Wiz spell fog cloud [conj] (PH 232), the 4th-level Sor/Wiz spell solid fog [conj] (PH 281)). I'd consider this despite such mechanics being usually reserved for, for example, spells with the light descriptor versus spells with the darkness descriptor (as the opposing spells mentioned in faerie fire rightly warrant), because the game makes overcoming fog hard, I like low-level spells being versatile, and this has always seemed to me what should happen when lower-levels spells encounter higher-level spells. (Thus if a player wanted to heighten faerie fire to a 9th-level spell to see his foe while the foe's in, like, an incendiary cloud, I'd totally let him.) As a once-in-a-blue-moon (once-in-a-pea-soup?) rule, though, this might be too much work for too little reward.