Unfortunately it isn't that simple. The poster has misunderstood your question.. You have 2 problems:
1. You need to feed the Slingbox input from the FireTV. You don't tell us what Slingbox you have, but unless you have a 500 you will need an HDMI > Component converter. I don't know if the HDMI output of the Fire TV is HDCP enabled, but if it is you will need a converter that also strips out the HDCP signal.
2. You have to control the Fire TV. Your problem is that the FireTV is Bluetooth controlled and the Slingbox works only with IR. So you will also need to buy some sort of IR to Bluetooth converter as well. I don't have any experience of those, but Googling it shows they are available.