I am not aware of any flash carts that are compatible with both the DSi and the Wii. (I just did a search too and turned up nothing.)
I currently use an Acekard 2 with my DS and they have just released an Acekard 2i for the DSi…reviews seem very positive and it’s stable and works well. You can pick one up for cheap at realhotstuff.com. Their shipping is fast!
correct me if I’m wrong, but you need to have a mod chip installed inside the Wii…I believe it won’t use flash carts like you’re talking about it. If I’m wrong, please correct me, I’m a new Wii user.