Yes, the new way currently only supports raw 16 bit, 44.1 kHz files. You can convert to raw using Audacity or SOX. Or normal 16 bit, 44100 Hz mono WAV files can be used as RAW format, if you're willing to accept a tiny glitch at the beginning or end, as the header and any extra non-audio data is "played" as raw data.
Eventually the new way will support other formats and the FIFO optimization, but it does work quite well without those.
To get files onto the flash, first copy them to a SD card. Then use File > Examples > SerialFlash > CopyFromSD, which copies the SD card to the flash memory.
Someday in the future, Teensy will support Media Transfer Protocol (MTP). When that happens, you'll be able to select MTP Disk in Tools > USB Type, and program your Teensy with an example that makes the flash chip accessible by MTP. Then with Windows or Linux, the flash will appear as a location where you can just copy files, without any need for the SD card step! Macintosh doesn't natively support MTP, but 3rd party programs exist to add MTP on Macs. One of the main reasons this new way was created is for that glorious MTP-enabled future!
The new way supports SPI transactions, so it will automatically play nice when used with things like nRF8001 and CC3000 and RadioHead (if using the Teensyduino version which has SPI transactions added) and other interrupt-based libraries which are updated with SPI transaction support.
SerialFlash also has support for non-Winbond chips, like the larger Spansion and Micron versions which have different protocols to support more than 16 Mbytes. It automatically detects which chip you've used.