Green’s Dictionary of Slang

rod (and float) n.

[rhy. sl.]

an overcoat .

Dly Mirror 1 Sept. 10/3: ‘A rod’ is a shortening of ‘rod and float’ which is rhyming slang for overcoat.
[US](con. 1910–20s) D. Mackenzie Hell’s Kitchen 120: Rod ... overcoat.
[UK]F.D. Sharpe Sharpe of the Flying Squad 332: rod : An overcoat or mackintosh.
[UK]D. Powis Signs of Crime 199: Rod Overcoat.
[UK]J. Morton Lowspeak.