I wrote in about this earlier. It seems the word has two meanings; the version that originated Australia or New Zealand combines "flash" (stylish) and "backpacker" and may refer to people who can afford expensive hotels but choose to stay in hostels. The second sense is traveling with very high tech gear for an extended time.
Flashpacking is packing very light for a long trip but with plenty of high-tech gear: laptop, digital camera (plus lenses and extra memory cards), smartphone, MP3 player. So far it seems to be jargon, but according to USA Today it has been in use in New Zealand for six years (http://www.usatoday.com/travel/destinations/2006-06-19-flashpacking_x.htm). The word is based on "backpack," and people who flashpack may either be traditional backpackers (i.e., college students) or older tech-savvy types, some of whom do freelance work (on websites, for example) from their travels around the world. Sentence: A flashpacker can travel around Asia for three months with just a carry-on and keep her blog up-to-date as she goes.