I couldn't find Bits and Basics Air-Dry Clay but ALL air-dry clays are flammable depending on temperature they're subjected to since they're usually made with paper products (including plant materials). There are some "mineral" based clays though, and minerals won't burn but no telling how much of the clay is actually minerals, and of course "mud" or pottery clay won't burn till it gets much-much hotter (hotter than a normal kiln).
Anyway, paper won't burn till the famous 451 degrees F (233 C), but if a flame or coils or anything but air is close enough to them (in an oven or around a candle, etc.), the temp would actually be much higher and things like paper/air-drying clays --except for mineral or earth clays-- would darken, scorch or burn.
As for polymer clays, we use them for making things like tea-light/candle holders and votives for them all the time, BUT we just make sure the actual flame isn't too close to the clay (and definitely not over it).
Polymer clays are cured at around 250-275 F usually so they can take that much heat** (though may emit a polymer smell over 200 or so), but if they're just an inch or so away from the flame they won't heat up very much. If we make a clay-only container for a candle though, we'd also need to put something heat proof at the bottom of the candle if we intended to let the candle burn all the way down.
Polymer clayers often "cover" glass votives/cups/etc to put candles in though, and that takes care of the bottom-of-the-candle problem if allowing candles to burn down, and glass isn't a great conductor of heat too so that's an additional buffer for the sides of the container.
Here are just a few examples of votives "covered" with polymer clay... most of these are over clear or translucent glass so the light shines through, but could also be covering opaque ceramic items:
http://www.polymerclaycentral.com/claypen_votives.html
http://www.artistcrafts.com/gallery/candles.htm
If you're interested in tutorials for covering votives with polymer clay, more examples, etc, check out at least this page at my polymer clay "encyclopedia" site:
http://glassattic.com/polymer/covering.htm
...under Glass & Ceramic, click on VOTIVES + LIGHT SHINING THROUGH
And if you want to make freestanding containers, bowls, boxes, etc., of polymer clay (in lots of ways), check out this page:
http://glassattic.com/polymer/vessels.htm
"Varnishes" can be water-based or petroleum-solvent-based, etc., so how much heat they could take without yellowing, darkening, burning, etc., would depend on the type mostly (sometimes on thickness too if you count bubbling). We "re-bake" polymer clay items covered with water-based (usually gloss) polyurethane, etc., all the time, but do use a slightly lower temp for a longer time (e.g., 200-250 F for 5-15 min).
**to the get "toxic fumes" from polymer clay, you'd need to actually burn the clay (at over 385 F) which would result in thick black smoke, a horrible smell, lots of coughing, and a black piece of clay! ...that would still be only "irritating" to the lungs though, not "toxic" in the true sense of that word
HTH,
Diane B.