After sussing that we were supposed to interpret the titular 'flowers' as:
A cryptic clue for 'RIVERS' (see my comment on the main question above),
I had gone on to wonder whether the area of interest was indeed:
INDIA, as confirmed by @hexomino via the printer's devilry of Hint 3 (The oval is 11 in diameter), although I had not solved that particular clue. My own flawed reasoning had been based on 'putra' in 'Brahmaputra' (a river in East India) sounding like the alloy 'pewter'.
This logic inadvertently led me to the answer for the missing 'flower' (I myself am the glorious one who brings in heat / A four-letter word is what you need!) being:
TAPI - a river of central India named after the goddess Tapati, the daughter of Surya the sun god and "mother-goddess of the south, the home of the southern sun where she brings the heat to the earth" (source: Wikipedia).
After the OP's hints and prodding (thanks!) I have now worked out that the directions might not strictly indicate the part of the country they are located in but rather their position in relation to the solution.
So WEST (To the West is of conquer, of victory,) is:
Shetrunjaya (a river west of the Tapi), whose name literally means 'victorious; one who overcomes enemies'.
NORTH (To the North is for leather laundry) is:
Chambal (a river north of the Tapi) since its ancient name was Charmanvati, meaning 'the river on whose banks leather is dried' (Source: Wikipedia).
EAST (To the East is a great river, alloy) is:
Mahanadi (a river east of the Tapi) since its name is a compound ('alloy') of two Sanskrit words: maha meaning "great", and nadi meaning "river".
SOUTH (To the South is big and tall, ahoy!) is:
Bhima (a river south of the Tapi) since its name in Sanskrit literally means 'big' or 'tall' (Source: Wikipedia).
And thus the riddle is (definitely!) complete!