Game day and case of dysentery is flushed (5)
I believe the answer is:
ruddy
'is flushed' is the definition.
(synonyms)
'game day and case of dysentery' is the wordplay.
'game' becomes 'RU' (rugby union).
'day' becomes 'd' (abbreviation for day).
'and' means one lot of letters go next to another.
'case of' suggests removing the centre (like emptying a case).
'dysentery' with its centre removed is 'dy'.
'ru'+'d'+'dy'='RUDDY'
(Other definitions for ruddy that I've seen before include "Looking healthy" , "Blooming" , "Healthy reddish complexion" , "Healthily red; sort of duck" , "Rosy" .)