There will be HDMI spec issues here because the Fire Stick 4K supports 4K @60Hz while the receiver supports up to 4K @30Hz and the projector just HD 1080p.
To avoid issues, set the output resolution of the Fire Stick to 1080p. You can also set the output resolution of the receiver to 1080p in its settings.
Some new 4K devices will take issue with older HD devices supporting older HDMI and HDCP specs. Auto settings all around may not work and manual settings in each device to match a lower specced receiver, TV or projector may be needed for everything to work.