Basic node image with ffmpeg package installed. Please find the image on dockerhub here. https://hub.docker.com/r/josgraha/node-ffmpeg/
This approach may save some time over incorporating this step into your Dockerfile directly. Although it is dependent on the node base image using Jessie (Debian v8) which is the default for now.
Because the node base image is based on Jessie, the setup-ffmpeg.sh script installs ffmpeg version with the following options enabled.
ffmpeg version 2.6.9 Copyright (c) 2000-2016 the FFmpeg developers
built with gcc 4.9.2 (Debian 4.9.2-10)
configuration: --prefix=/usr --extra-cflags='-g -O2 -fstack-protector-strong -Wformat -Werror=format-security ' --extra-ldflags='-Wl,-z,relro' --cc='ccache cc' --enable-shared --enable-libmp3lame --enable-gpl --enable-nonfree --enable-libvorbis --enable-pthreads --enable-libfaac --enable-libxvid --enable-postproc --enable-x11grab --enable-libgsm --enable-libtheora --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libx264 --enable-libspeex --enable-nonfree --disable-stripping --enable-libvpx --enable-libschroedinger --disable-encoder=libschroedinger --enable-version3 --enable-libopenjpeg --enable-librtmp --enable-avfilter --enable-libfreetype --enable-libvo-aacenc --disable-decoder=amrnb --enable-libvo-amrwbenc --enable-libaacplus --libdir=/usr/lib/x86_64-linux-gnu --disable-vda --enable-libbluray --enable-libcdio --enable-gnutls --enable-frei0r --enable-openssl --enable-libass --enable-libopus --enable-fontconfig --enable-libpulse --disable-mips32r2 --disable-mipsdspr1 --disable-mipsdspr2 --enable-libvidstab --enable-libzvbi --enable-avresample --disable-htmlpages --disable-podpages --enable-libutvideo --enable-libfdk-aac --enable-libx265 --enable-libiec61883 --enable-vaapi --enable-libdc1394 --disable-altivec --shlibdir=/usr/lib/x86_64-linux-gnu
libavutil 54. 20.100 / 54. 20.100
libavcodec 56. 26.100 / 56. 26.100
libavformat 56. 25.101 / 56. 25.101
libavdevice 56. 4.100 / 56. 4.100
libavfilter 5. 11.102 / 5. 11.102
libavresample 2. 1. 0 / 2. 1. 0
libswscale 3. 1.101 / 3. 1.101
libswresample 1. 1.100 / 1. 1.100
libpostproc 53. 3.100 / 53. 3.100