I generally use about 22%, which is actually low on the scale historically - say 100 years ago. I'm not sure I get an actual corn flavor but I do think it gives a corny sweetness, as contrasted to when I use rice, which seems to give a drier, crisper beer. George Fix agreed (actually, I agreed with him.)
But who knows? At the 2000 National Homebrewers Conference in Livonia, Michigan, where I gave a talk on CAP, retired Stroh Brewery brewmaster (and inventor of the Beer Flavor Wheel) Morten Meilgaard also spoke, and was very insistent that corn and rice were neutral in flavor!
Stroh's archivist Peter Blum also spoke. He told me that Stroh's used rice until the 1950s, then corn until the 1980s, when they used brewers corn syrup (with the same sugar spectrum as mashed grain).
Rice was preferred by many brewers of 100 years ago because of the reputation that milled corn had had of having too high a proportion of oil, which would go rancid and spoil the quality of the beer. Advances in dry milling of corn eliminated this problem, but Stroh was a very conservative, family owned business according to Blum, and stayed with rice long after most brewers had switched to corn.
Both Blum and Meilgaard were quite definite that there was no flavor difference in corn, rice and corn syrup. They definitely knew their business, and spoke from experience with tasting panels.
My experience differs. Maybe our scale leaves more flavor from the corn?
At any rate, in answer to the original question, 20-30% corn should give corn character. Make sure that your flaked maize is fresh and has a corn aroma. Doing a cereal mash with corn meal or polenta might help. Beside, it's fun.
One further question is, were you tasting DMS in those samples you've identified as having corn flavor? That is different, and can be appropriate in small amounts. It was typical of many midwest beers before modern techniques cleaned it up.