Nintendo's apparently confirmed that DSi will have 256Mb of internal Flash memory, according to this IGN report.
From the piece:
The only piece of content available under the DSi Ware option at the moment is the free Opera browser. The download takes 85 blocks of your 1,024 block space. While not listed in the system's official specs, Nintendo president Satoru Iwata said during a recent investor briefing that the internal memory consists of 256 megabytes, which is half that of the Wii.
Reggie specifically declined to confirm how much internal memory the machine would have at the time of its announcement.