In general, one should not wear clothing inside-out, as per Shulchan Aruch, OC 2:3:
ידקדק בחלוקו ללובשו כדרכו שלא יהפוך הפנימי לחוץ
One should be particular with his cloak to wear it properly, that the inside not be flipped outside.
As the Magen Avraham explains (§3):
ויראו התפירות המגונות
And they will see the disgusting stitches
May one wear his clothing inside-out on Purim, as (a part of) his costume, where the whole point is that one should not be dressed as he normally is?