Interface ADCs using Multiple SPI connections

Hello I want to use an arduino to read data from 2 ADCs (MCP3008). At some points I may want to run the ADCs at 10kHz per channel, which will bring in a total 160 000 sample per second. Can this be done? Is it tricky?

I want to pipe all this data into flash memory/an SD card reader? Again, this uses SPI, am I sill ok?

I have a few Unos lying around, will this be sufficient or do I need to use another Arduino?

Well, SPI is the only way you'll get there. Storing more than 40K samples might be difficult.
Google fat16lib's code hosting (github?), I think he has managed 100K.