How to encode Apple ProRes on Windows or Linux?
As of December 2018, Adobe Creative Cloud aps, such as Premier, After Effects and Adobe Media Encoder give you the ability to encode in ProRes without any post-hoc conversion.
If you don't use Adobe CC aps or want a free, open source tool, ffmpeg can encode video using ProRes, and runs cross-platform. ffmpeg is a command line tool, which means that it can be automated.
There are a plethora of free GUIs for ffmpeg for those unfamiliar with the command line.
This ffmpeg command:
ffmpeg -i input.avi -c:v prores_ks -profile:v 3 -c:a pcm_s16le output.mov

will do the trick.
The -profile switch takes an integer from -1 to 5 to match the ProRes profiles:

-1: auto (default)
0: proxy ≈ 45Mbps YUV 4:2:2
1: lt ≈ 102Mbps YUV 4:2:2
2: standard ≈ 147Mbps YUV 4:2:2
3: hq ≈ 220Mbps YUV 4:2:2
4: 4444≈ 330Mbps YUVA 4:4:4:4
5: 4444xq ≈ 500Mbps YUVA 4:4:4:4

The approximate bit-rates are for 1920×1080p footage. All of the profiles are progressive, 10-bit, and little-endian (byte order).
The profiles are explained on the Apple website. There doesn't as yet seem to be support for RGBA encoding in 4444 and 444xq which the official Apple codec supports.
You may also use prores instead of prores_ks, which may be a little faster, but does not offer the 4444 profiles. For more background, please read this FFmpeg Wiki article.