Is the one necessary in cases like these?
The machine had a lumpy side and another flat (one).
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"Another" is a determiner of difference so you need a noun or noun phrase to follow. "Flat" is presumably an adjective (assuming you are not describing something like a flat tire---often referred to as a "flat") so you need the "one" to follow. However, if you did have a noun following the "another" you could say:
"The machine had a lumpy slide and another widget."