Blink, to shine briefly or to briefly close one’s eyes (as though something just shone in them) occurs a handful of times in the work.  It may come through Old English blican.  Yet there is a different meaning.  The Online Etymology Dictionary explains that Tom the Troll’s use of “blinking” in Chapter 2 “as a euphemism for a stronger word” is attested by 1914.

• 01.044 he said, blinking.
• 02.045 “Never a blinking bit of manflesh
• 04.044 The blink of red torches could be seen
• 05.087 and made his eyes blink
• 05.136 Bilbo blinked,
• 06.067 that could look at the sun unblinking,
• 08.042 and blink.
• 10.028 and stood blinking

Harper, Douglas. “Blinking”.  Online Etymology Dictionary. Web.