The Killers frontman, whose record consists of tracks originally intended for the band, managed to knock last week's number one, Katy Perry's Teenage Dream, into the runner-up spot.
The feat means that Flowers keeps his 100% track record of releasing chart-topping albums, following The Killers' three number ones Hot Fuss, Sam's Town and Day And Age.
Number three this week is The xx's Mercury Prize-winning self-titled album, which climbs 13 places to enter the top five for the first time in its 56 weeks of release.
The Top 10 also sees two more new entries in the form of Happiness by Hurts at four and Stone Sour's Audio Secrecy at six.
The debuts continue outside of the upper portion of the chart, as Ray LaMontagne & The Pariah Dogs reach 17 with Good Willin' & The Creek Don't Rise, just ahead of The Morning After by James at 19.
The Top 10 in full:
1. (-) Brandon Flowers: 'Flamingo'
2. (1) Katy Perry: 'Teenage Dream'
3. (16) The xx: 'The xx'
4. (-) Hurts: 'Happiness'
5. (2) Eminem: 'Recovery'
6. (-) Stone Sour: 'Audio Secrecy'
7. (3) Biffy Clyro: 'Only Revolutions'
8. (4) Mumford & Sons: 'Sigh No More'
9. (-) Eliza Doolittle: 'Eliza Doolittle'
10. (8) Lady GaGa: 'The Fame Monster'
Source: Official Charts Company
> Click here for this week's singles chart