No. Although they are etymologically related, the two words do not have the same meaning in modern language. Kleid is specifically a dress. The plural is still used for the older, more general “garment, clothes” (you will also hear Kleidung (f.) or colloquially Klamotten (f.pl.)). But the singular Kleid is not used in that general meaning, except in rather poetic speech, and even then mostly figuratively (for example a bird’s plumage can be called Federkleid). Neither singular nor plural is ever used for pieces of cloth (that is called Tuch (n.)).
I wrote 'the dress is neat' and it was rejected what's the difference between neat and clean in german
sauber means “unsoiled, unstained, not dirty” (or when we’re talking about liquids or gases also “clear, pure”). So ein sauberes Kleid means a dress with no stains. If “neat” can mean that in your dialect of English, then yes, it should be accepted. But if it basically means “orderly, tidy”, that’s not sauber in German but ordentlich.
Because Kleid means “dress”. “cloth” (as in the material) would be Tuch or Stoff.