How close is the CDS (January 14, 1928) to the first day of issue?
From wikipedia:
"A British-backed monarchy joining these vilayets into one Kingdom was established in 1921 under Faisal I of Iraq. The Hashemite Kingdom of Iraq gained independence from the UK in 1932. In 1958, the monarchy was overthrown and the Iraqi Republic created."
Gibbons states that the set was issued between June 1, 1923 until 1925. Scott, in the classic catalog says the set was issued from 1923-1925. Michel says the set was issued between 1923 and May 1925.
So, putting all three catalogs together (sheesh!), the set was issued from June 1, 1925, through May 1925. None of the catalogs give an issue date for any individual stamp in the set. You'll most likely need a specialized catalog/collector for that information.
The SG standard is that the date shown (in this case 1 June 1923) is the date the set was issued. Any subsequent issues in the set show a separate date. You can assume that 1 June was the date of issue