Different folks on here use "incomplete flush" to mean different things.
Some folks, having been for the first time exposed by we of this forum to the wonders inside their tank, suddenly start complaining that the flapper "closes too soon unless I hold the handle down", because they suddenly discover that the tank isn't draining completely, which they call an "incomplete flush". Actually, when it does that it's doing what it's supposed to do.
Others, who already know that modern toilets don't drain the whole tank, complain about the flapper closing too soon and causing the water in the BOWL not to cycle (i.e. the poo doesn't go down). In other words, it's not doing what it's supposed to do, which is to drain about a half of the tank. They call THAT an "incomplete flush". And that's probably an accurate description of that. Sometimes, when my hand slips off the Drake handle or I don't depress it fully and release, the flapper kind of half-opens and slams shut before releasing a fraction of what it usually does, and the bowl starts to fill and then starts to siphon and then stops, with all the ickyness floating in it. I call that a "misfire", which can be resolved just by pushing the handle all the way down and immediately letting go (after, of course, the tank refills).
Terry's testy retort was addressed to the folks who fall into the first category above. I'm not sure from your description whether you do or not, so this is for you if you don't:
Sometimes, too LITTLE chain on the flapper can prevent it from opening fully, along with other evils. Not so much on our Drake, but certainly on my AS in the city, if I change the flapper, I have learned to always hook the exact same number of links to the arm. Too few, and it blocks the flapper from opening all the way, leading to a non-optimal result. Too many, and it doesn't pull the flapper all the way open, leading to the same result. Just right, and it works just right. Generally, a link or at the most two lying on top of the flapper is about right. Very little slack, but some slack. Yours looks too taught. So if it's misfiring, then add a link. If you can't because that old tilt-flush thingy is out of chain, you can replace that tilt-flush with a Korky flapper and then adjust the chain to your heart's content.
Terry, whom I trust, says that that's an Ultimate, which would be MS854114. The UltraMax is 854114S, which you say yours is. If it's the Ultimate, then you use the BLUE Korky Fits Toto Flapper (#2022). If it's the UltraMax, then you use the RED Korky Fits Toto Flapper (#2021). Both available at Home Depot online, and other fine stores.