Impossible to not measure curvature, but possible to make it harder to see
The biggest planet detected so far is HAT-P67-b - being twice the diameter of Jupiter with a diameter of around 147000 km. It is this large only because its density is so low.
It is unfortunately a gas giant. Currently our planetary formation theories only support planets that large to be formed as gas giants. Any larger diameter, depending on density, would create a star instead as its inner core would be dense enough to enable fusion. A brown dwarf star can be formed in gas giants that are only slightly bigger than Jupiter.
You could argue Gas Giants do not have a 'horizon' in the same way rocky planets do, they are 'diffuse' and it would be difficult to perceive any radius as you are simply surrounded in gas.
However if restricting to rocky planets our radii are much smaller.
Kepler 10c is the largest rocky planet we have found, with a diameter 2.3 times Earth, about 29000km. This could be the very upper limit of a rocky planet. It's radius, being only twice as big as Earths, is much smaller than a gas giant, and you would still perceive the radius of this planet at a high enough altitude (or really mathematically at any altitude).
However - many things contribute to perceiving curvature. We can see curvature on an ocean at a height of only a few meters, by using a telescope to see a ship come over the horizon, but this is difficult to perceive on land because the irregularities in hills, mountains and surface features dilute the curvature such that we cannot perceive it readily. Perhaps this is a more realistic way to conceal curvature by making hard to perceive, rather than by size trying to make it large.