Adafruit Huzzah and SD card breakout
From experience, I know the following


Using two SPI devices sometimes does not work, especially with fake SD breakout cards. Not sure about an Adafruit, but try to use only one SPI device at the same time (to check if it works better). For my project (initial setup), I had to use a SD logger extension board instead. 
Sometimes it depends on the SD card which will work. Try to use older non SDHC/XDHC cards (smaller storage normally).
Use the most simple (and preferably example circuit) to test each component separately (thus your SD breakout card) before adding others (like the WIFI component). This rules out there is no problem with other components working at the same time.