Green’s Dictionary of Slang

1. to talk loudly, to complain, to make a fuss.

1932

(con. 1910s) J.T. Farrell Young Lonigan in Studs Lonigan (1936) 105: Come on an’ quit dynamitin’.

2. (Aus. gambling) of a bookmkaer, to set over-long odds.

1915

Drew & Evans Grafter (1922) 47: He’ll never have a good winning day if he dynamites them the way he is doing now.

3. to talk in an aggressive manner, esp. when trying to sell something or seduce someone; thus dynamiting n.

1930		D. Hammett Maltese Falcon (1965) 300: Well, don’t dynamite her too much.
1956		‘Toney Betts’ Across the Board 240: Touts were allowed to advertise winners they did not have. This was called ‘blasting,’ ‘dynamiting,’ or ‘bulldogging’.
1959		H. Ellison ‘Have Coolth’ in Gentleman Junkie (1961) 131: So I took the Tiger down to see Frankie Sullivan [...] and in a burst of frantic dynamiting, sold him on the kid.

4. to push something through, to make it happen fast.

1938

‘Aeroplane Factory English’ AS XIII:2 156: dynamite an order. To rush an order through as quickly as possible.