Green’s Dictionary of Slang

skating rink for flies n.

a bald head.

1887		Lawrence Dly Jrnl (KS) 12 Apr. 4/5: The best seats in a theater are those just back of the ‘bald-headed row.’ It is much easier to squint across the shining expanse of ‘skating rink’ the go through the gymnastics necessary to obtain a view from behind [...] a hat.
1913		‘J.W.L.’ Slave Stories 45: As bare of type as his own ‘flies’ skating rink,’ to use the office-boy’s description of the shining dome of hairless pate.
1926		Maines & Grant Wise-crack Dict. 14/2: Skating rink for flies – Baldheaded man.
1960		A. Burgess Doctor Is Sick (1972) 196: Some lovely bonces here tonight [...] Real skating-rinks for flies.