The flag of the Pitcairn Islands has an aspect ratio of 1:2. It consists of a blue field with the Union Jack in the top left corner and the coat of arms positioned on the right side. To provide specific color codes:

1. Blue - Pantone 280 C, HEX #012169, RGB (1, 33, 105).

The geometric properties and measurements are as follows:

1. The Union Jack covers a quarter of the flag's area, occupying the top left corner.
2. The height of the coat of arms is equal to half the height of the flag, and it is positioned at the center of the right half of the flag.

Due to the knowledge cutoff date of September 2021, I am unable to provide more detailed information on the exact geometry or measurements for the coat of arms elements.