I don't think 'flee about' is a typical collocation. Several of the examples are pretty unusual.
In the Tennyson poem 'The Kraken' from your other thread, the context for your first example sentence,Siehe auch: The Kraken sleepeth: faintest sunlights flee ...http://www.naic.edu/~gibson/poems/tennyson1.html
which I assume is still the basis for your question, I think you should read it as 'flee' (pause) 'about his sides,' meaning around him. I would also say that the sense 'vanish' seems like a reasonable primary reading, but there may also be shades of 'fly,' 'flit,' 'float,' 'be fleeting,' etc., and possibly also 'run away,' 'shy away,' 'flinch,' etc. The whole point of poetry is that poetic language can evoke more than one meaning. Tennyson probably chose the word at least in part for the rhyme, but partly also because it has this interesting range of meaning, as fluid and tenuous as the rays of sunlight themselves.
I won't take time to look in the OED, since people already did that in the other thread, but I assume the 'vanish' sense is also recorded there.