I don't have experience with any of the Wii hardware. The requirement for FSPDS to run is a DS system/emulator/virtual console with access to a FAT filesystem. For now, if we can't make stuff work on things they weren't designed for, let's just hope a flipnote viewer is ported to a wider variety of devices in the near future!
Hi! Maybe this works for you:
https://notimplementedlife.github.io/FSPDSNitro/
You can make FSPDS not depend on the filesystem if you include the flipnotes in the NDS ROM itself. The link above directs to a page where you drag-drop a bunch of PPM files and download a NDS file that should see and play them. If that was the cause of incompatibility with the Wii U, then this should solve it. Please let me know whether you succeed or have any issues with it.