... ends oddly with A Study in Scarlet getting flushed (8)
I believe the answer is:
reddened
'flushed' is the definition.
('redden' can be a synonym of 'flush')
'ends oddly with a study in scarlet' is the wordplay.
'ends oddly' becomes 'de' (I can't justify this - if you can you should believe this answer much more).
'with' means one lot of letters goes inside another.
'a study' becomes 'den' (I've seen this before).
'in' is an insertion indicator.
'scarlet' becomes 'red' ('red' can be a synonym of 'scarlet').
'de' placed around 'den' is 'ddene'.
'ddene' inserted into 'red' is 'REDDENED'.
'getting' is the link.
Can you help me to learn more?
(Other definitions for reddened that I've seen before include "Blushed colourfully" , "Blushed, became flushed" .)