Are there any cameras that are capable of taking video that would work the the TinyDuino?

I would like to take a few minutes of video, saving the file to the SD Card.

So would something like VC0706, VC7670, or cc1563 work?

Thank you

Hi Nefariis.  That sounds like an interesting project, especially considering that there is 32KB of total SRAM available to the processor of the TinyScreen+ or TinyZero.  A single 16-bit 160x120 QQVGA camera frame will use 38,400 bytes of RAM (160x120x2 bytes).
This won't fit in whatever is left of your 32KB of RAM with the app loaded.  So recording video with this board will require writing partial frames.

Thus you will be working with frame blocks.  Maybe these blocks could be compressed slightly with a very lightweight compression function to use less bandwidth, e.g chroma sub-sampling.  At 48Mhz you will have ~3.2 million CPU cycles per frame to play with (ignoring any waits for I/O, etc).
Alternatively there are cameras that can do various types of compression for you, chroma sub-sampling, M-JPEG, h.264, etc.

The data rate for uncompressed 16-bit 15fps QQVGA will be 562.5 KB/s.
Overall the SPI-interfaced microSD card will have to be able to maintain the block write rate otherwise you will lose frames.

This reference design might help with some of the work: http://www.ti.com/tool/tidm-tm4c129camera