unless you are mass producing, you will not save anything using atmega328 chip and building your circuit. you can get an arduino pro mini now for $3.45 and can use the full 32kb program space if you program via icsp.
anyway, if you are doing animation, is that at 15 frames per second? or probably slower right? at 15 frames, that gives you 66ms to setup the data and send it out.did you try this at all yet? sd read should take a shorter time that sd write. worse case you can use timer interrupt code to control your led line, reading from a circular buffer containing the frame data, and the sd card read will be in the main loop just continuously filling up the buffer.