High Speed Embedded Memory

Assuming Ethernet and USB are out of the question (hitting 40MB/s should be possible with both). If connecting over a cable is possible this probably becomes a lot easier (and cheaper too).

But if you must locally store it first how about multiple flash interfaces that each are responsible for 'x' number of ADC channels of storage? Then you can access them concurrently to eliminate the bandwidth problem. I would check to see how much bandwidth you achieve with a single flash channel then scale it up accordingly so that you can try out different solutions easier.

What do you have in mind after you are done storing the data? Would you just pull flash cards out and bring them to a host or would you move the entire board and download the contents after? You'll probably require fewer flash interfaces if you just need the later (download from the board) since soldered down devices are usually quicker than cards (unless you use a complicated controller and fast/expensive cards)