Nintendo has confirmed to MCV (linked above) today that flash cards such as the R4 will not with the Nintendo DSi.
This news does not come as a shock to most, and was suspected by many Nintendo DSi owners who reported on it last week.
To quote: Nintendo has confirmed to MCV that today's reports claiming that SD-card based piracy hardware the R4 will not work with the upcoming DSi are correct.
The platform holder was not able to confirm whether this is a deliberate feature of the newly redesigned handheld. However, judging by recent history it's not unreasonable to presume this is the case. More PlayStation 3 News...