I must have a fling at.. Throw a stone at something. To attack with words, especially sarcastically. To make a haphazard venture. Allusion is to hurling stones from slings.
“If he is young, he desires to have his `fling' before he is compelled to settle down” —Nineteenth Century (February,1892, p. 208).
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894