Well, I found TXC0. It's in register UCSR0A. I assume it is accessed in the same manner as the SPIF flag, so the equivalent to:
while(!(SPSR & (1 << SPIF)));
Would be:
while(!(UCSR0A & (1 << TXC0)));
Though the docs seem to indicate that it is not necessary to wait for the byte to be transmitted with the UART because it has a buffer.
That's another reason I recall now that I put the SD card on the UART. I thought I would be receiving more data from the SD card than I would be transmitting to the DAC and my LEDs, so I thought the buffer might improve performance. Now however I'm not so sure. I'm not sure that the buffer applies to receiving data or that if it does there is any benefit. It may have been more beneficial to use it for transmitting data to the DAC and TLC5947's I have hooked up.