The flag proposal looks approximately like this:
The flag in question was initially proposed in a booklet called Fylkesmerker (1930), by Norges Bondelag (Norwegian Agrarian Association), that presented proposals of coats of arms and flags (always banners of arms) for each Norwegian region, some of them adopted with small changes. The only explanation for the design by heraldist Hallvard Trattberg on the book is:
Riksløven på gråverk (heraldisk pelsverk) for å betegne gammelt norsk land.
What means, in English:
Norwegian lion in vair (heraldic fur) to denote old Norwegian land.
In fact, the lion is identical to the one present on Norwegian coat of arms. Although there isn't presented, in my understanding, a clear rationale to background of vair (better blazoned as "vair in fess", in this particular case), my (unsourced) theory is that it's a clever reference to blue and white landscape of this icy archipelago, and a association between a fur (in the case, squirrel fur) and the cold climate. If this theory is true, I think this proposal was very well-though, and could be a winner once Svalbard needed a flag.
Until then, it's only one more flag that exists only on internet..
Your comments are welcome.