Not much of anything, on one hand he can gain moderates (of the Stevenson and Parker mold) who stayed with Bryan even while not believing in the rhetoric of the Populists, but at the same time he's facing a good amount of unpopularity and is trying for a third term. Perhaps a slight gain for the Gold Democrats but as that party was working as an annex of the GOP, the gains will be aimed to hurt Bryan more, where they can get them.
After that, the Gold Democrats and Bryan himself are probably all beaten down for the running in 1900.
The thing is, despite Cleveland being unpopular, he would have had access to the main financiers of the Democratic Party at that time, who in OTL refused to contribute any funds to Bryan's campaign, and may have very likely instead funded McKinley. For example, the Democrats in 1892 managed to gather together $2,350 thousands of dollars, while in 1896 they only managed $675 thousands. The Republicans on the other hand in 1892 had taken in $1,700 thousands, while in 1896 that amount increased to $3,350 thousands. It is possible that a lot of the financial power within the Democratic party could have sat out entirely, but the data does hint to aforementioned idea.
You would also have the German and Irish Democrats likely remaining, in least in large part, with Cleveland given they would be alienated by Bryan's policies and now have another choice beyond McKinley. I'm not certain exactly how prominent they would have been in certain regions at that time, but that would certainly lock Bryan out of the Northeast entirely if not eliminate him, and would remove parts of the Midwest from contention.
Labour workers, despite being a core Democratic constituency at that time, would likely still go for McKinley though by a smaller margin. Cleveland during the last four years of his tenure would have managed to alienate them given his conduct during the various strikes conducted on his watch, while they were just as wary of Bryan given their opposition to the proposals of Free-Silver.
McKinley would win, but I'm not actually certain which way to the South would go; Cleveland or Bryan?