Connecting multiple boards to Arduino Uno r3
Short answer: yes, you can. No pin conflict, but you will need an extra SS pin for the second SPI device. [If you can, use the I2C version of your device.]

Unlike the I2C, the SPI bus uses separate lines for sending and receiving data, and it employs an additonal line (SS, SS1, SS2, ...) for selecting which slave device you are talking to. This adds additonal wires, but also eliminates needing different slave device addressses. So what this means is instead of specifying the address of the slave device, we simply address that slave device by turning on its SS pin. It's a lot more simple.

So, if you have two devices (RFID reader and SD Card Adapter), the conections looks like this:



The thing is, you need to use two Arduino pins for selecting the devices you want to talk to: one pin select the RFID reader; the other, the SD card.

Arduino has a fixed pin assignment for SPI comunications:



Because all devices share the MOSI, MISO, and SCLK lines, all commands sent from the master arrive at each slave device. The SS pin tells the slave whether it should ignore this data or respond to it. Importantly, this means that you must make sure to only have one SS pin LOW. 

So you can see now how it's a minimum of four data lines that must be present in any SPI system. The MISO, MOSI, and SCLK signals are shared common with all slave devices. However, the SS chip cannot; it must be separate, because each slave device needs its own unique connection so that it alone can be addressed when the master device wants to communicate with it. So for each additional slave device that you add, you must have an additional line available on the master device for that slave device. So, using the above diagram as an example, if we have added a third slave device, we would have to add another SS3 data line to the master device and then connect to the SS pin of that third slave device.