I'm hoping you have this figured out, but if not-
The Flirc does not need Amazon codes sent to it from your remote. When you are programming the Flirc you choose which of the device you are connecting it to (Fire, Shield, X-box, etc) and it will send the correct code thru usb to your Fire.
First you need to load the codes from a chosen component in the data base to the MX-990. It doesn't matter which component in the MX-990 data base you choose. For my Nvidia shield I chose the codes from a Sony DVD since I do NOT have any Sony components that might respond to a Sony IR command. You then open the Flirc program on your laptop, connect the flirc to a usb port on your laptop and follow the Flirc setup as it goes from button to button on the Amazon Fire remote picture on the setup screen.
The correct codes are built into the Flirc program for the chosen component you want to control. The Flirc responds to the loaded command from your remote and 'translates' it to the correct command to the Fire.
Sorry if I've made this sound complicated. It's not. Flirc has done the heavy lifting. You just need to program your remote with any IR commands then program the flirc on your laptop with the Flirc software/program and then move the Flirc to the Fire.