Flower that's split, right? (5)
I believe the answer is:
river
'flower' is the definition.
(A river flows and is therefore a flower)
'split right?' is the wordplay.
'split' becomes 'rive' (synonyms).
'right?' becomes 'r' (common abbreviation).
'rive'+'r'='RIVER'
'that's' acts as a link.
(Other definitions for river that I've seen before include "Thames is one" , "Tees, perhaps" , "One splits" , "Dee, Exe or Wye, say" , "course of 1d [ADVENTURE]" .)