- several people here mention that they learned this phrase in the military
- the first written mention I could find is in a 1998 army report [0]
- the first Google Books hit for this phrase is from 1970 but this seems to be an error - the full text preview is from a different, recent book [1]
- Internet Archive has a lot of hits - but the earliest ones - except for the army report mentioned above - are from the 2000s (don't be fooled by wrong publishing dates in the metadata) [2]
- Google Ngram Viewer shows a brief appearance around 1980 (maybe a fluke) and then a steady rise in the 2000s [3].
- In one army magazine I saw an extended version: "slow is smooth, smooth is fast, fast is deadly" (which doesn't transfer that well to other professions)
[0] https://archive.org/details/DTIC_ADA357718/page/23/mode/2up?...
[1] https://www.google.de/books/edition/Span_of_Control/IYy_EAAA...
[2] https://archive.org/search?query=%22slow+is+smooth%22&sin=TX...
[3] https://books.google.com/ngrams/graph?content=slow+is+smooth...