Looking at a list of which shows were airing at the time these Flava dolls were “popular” does not really follow this idea of Nickelodeon promoting “girl power.”
A quick Google search shows that the selection of shows during this time includes there is a huge number of anthropomorphic animals (coming of age type of stuff) and these characters are primarily male.
Shows with girls, possibly in a more “girl power” light includes: Totally Spies, All That (?), Dora the Explorer, Power Rangers, Maggie and the Ferocious Beast, My Life as a Teenage Robot, The Wild Thornberrys, As Told by Ginger, Rocket Power
But consider the representations of girls in these shows: most promote that you can be smart AND pretty/girly, or they are secondary, supporting characters struggling for heterosexual relationships, often surrounded by groups of male counterparts. If the girl is the star of the show, then a male character of some sort must accompany her. All of the examples I have listed follow this idea exactly.
So yes, I guess Nickelodeon was promoting “girl power” in 2003, but only as much as 60s/70s feminists were promoting equality. Both are problematic, especially where representations of class, race, etc. are concerned. In a way, the commercial for the Flava dolls is an accurate representation of Nickelodeon at this time period.