The 六国史 (rikkokushi) (six national histories) is a series of 6 books detailing the early history of Japan. I need to know where I can download English translations (I can't speak old Japanese) for a project on my server, you can see my progress here.
Plain and simple answer: translations into English past the first of the six chronicles do, from my knowledge, not exist.
However, the Shoku nihongi and the Nihon kōki were (only!) partially translated to German back in the 1962, as Rikkokushi: Die amtlichen Reichsannahlen Japans, translated by Bruno Lewin.
Otherwise, the most easily digestable you could get would likely be translations into contemporary Japanese.
Unfortunately, the state of translation of premodern Japanese sources to European languages is, in general, still very selective. And many of the translations that exist have been produced in the 1960s or 70s and are hard to get by nowadays.
The exception form works of literature and poetry, which, I suppose, are an easier sell.