The BioLite looks interesting, but unsure if shipping or real product yet. Output is something like 2 watts at 5V (USB). That is paltry considering they claim the fire is like 3-5KW of energy.
Themoelectric elements are available on Ebay. Go looking and shopping. They are also called: TEC's, TEG's, Peltier Power Modules, Peltier Cooling Plates, etc.
TEG's are two sided. One is hot, one is cold when operating. So you can create heating devices as well as cooling devices or apply heat to one side and get a SMALL electric charge.
In order to use a TEG near fire you need to affix a water reservoir to prevent the element from overheating. That water needs to circulate or it will overheat and cause failure of the element. Yes, you can heatsink them and use a fan for blowoff instead. Both require power, further drawing down your generation of power pool.
My opinion is TEGs are only viable when you make your own setups and combine these into gang units. Cost is too high per watt and power generation numbers are too low with commercially available units, so far. The elements are downright cheap and often can be found perfectly fine used or scavenged from 12v fridges, wine coolers, etc.
This is a company here in the USA making products available now:
http://www.tegpower.com/index.htmlThis is a similar product that siphons electric from a gas lantern:
http://www.tegpower.com/pro9.htmComplete product list:
http://www.tegpower.com/products.html