There are plenty of AppNotes on the DMA. They also show exactly how to transfer ADC results with DMA to memory. (I think for the -050 kit the sample program even worked that way and showed the result on the LCD; but I might be wrong)
EEPROM writing is very slow operation, size is limited (2k) and writing can be only in raws (16? bytes). How DMA fits into this? You may save ADC data to memory using DMA and then transfer it to EEPROM for storage using CPU.
It would be advisable to save the data in SRam, not in EEProm which really needs programming. When you want to save data over a power-down you may use some external memory like FRam or an sd-card. FRam is available on the CY8CKIT-044 board.