Flat perhaps and neat, the last few yards (4,8)

I believe the answer is:
home straight
'last few yards' is the definition.
I don't know anything about this answer so I can't judge whether it can be defined by this definition.
'flat perhaps and neat' is the wordplay.
'flat perhaps' becomes 'home' (I can't explain this - if you can you should believe this answer much more).
'and' says to put letters next to each other.
'neat' becomes 'straight' (synonyms).
'home'+'straight'='HOME STRAIGHT'
'the' is the link.
Can you help me to learn more?
(Other definitions for home straight that I've seen before include "Last part of a race" , "Final stage of a racecourse" , "final stage of race" , "Last stage of race" , "covered in neat report" .)
