The strategy to make a FLAG-free cloning is dependent on the plasmid itself (location of the tag, availability of cloning sites upstream/downstream of the tag). For instance if the tag is meant in the plasmid to be at the 3' end of the cloned ORF then inclusion of a stop codon within the reverse primer used for cloning is enough to get rid of it.
Tell me what the plasmid is and I might be able to help you more.
As Dominique said, it depends much more on the plasmid itself than on the segment you want to remove (although stopping its translation with a stop codon should work).
If you have restriction sites on both ends of the segment in question I find that a very effective approach is to digest at those sites and then insert a small oligo to close the plasmid, you can see how this can be done here https://www.addgene.org/protocols/annealed-oligo-cloning/.
This actually can work even if you don't have restriction sites perfectly positioned. If you have sites within the segment itself and only that, it is still very likely that the removal of only a part of the segment and insertion of oligos will still shut it down effectively.
Of course there are other options, if you include the map of the plasmid maybe we could advise more directly.
The easy way to remove it is to use site-directed deletion ( protocol details see the link and the attached lab protocol)Article An efficient one-step site-directed deletion, insertion, sin...