Green’s Dictionary of Slang

act the linnet v.

[SE linnet, a song bird]

(Irish) to flirt.

[Ire]L. Redmond Emerald Square 143: Sloppy Molly was nuts about her father’s new assistant. Nobody ever caught them acting the linnet or anything like that, but it was the very lack of any bit of flirting in public, that put them on to Molly.