It runs like smoke and oakum; a familiar way of saying, that a story, piece of news, a fire, &c. has spread about with the utmost rapidity, or, as we say, has run like wild fire. Het run lijck (gelijck) molken aen de kom ; q. e. it run like milk into curds, it went off as suddenly and rapidly as curds run together, when milk turns ; and, as every one knows, the coining of the curds when milk is in a state to produce them, is rapid, sudden, and general, as regards the mass of milk acted upon ; and may thus, not inaptly, serve for a natural type of rapid, sudden, and general spread of effect, especially in a familiar and rather jocular phrase.
Molken is milk-stuff, prepared or intended for the making of cheese and other dairy produce. Runnen is to turn into curds, to turn sour, whence our to run in the same sense. Molken has the sound of miolken, and is grounded in the Gothic or Islandic miolk, the Swedish mioelk , the Dutch rnelk, and our milk ; and it is this sound of oik as iolk that makes the oke in smoke ;
kom is dairy-pan.
Source: An essay on the archaiology [sic] of popular English phrases and nursery rhymes 1834