What pattern maximises a JPEG file's size?
Pursuing on @OlliNiemitalo, JPEG allows some loss related to frequency quantization. So any file can be compressed to any size, hence you cannot maximize a JPEG size without setting some constraints, like quality. Let us assume a standard metric, like mean-squared error.

Now, let us check some of the JPEG features for image sparsification, and let us try to go the opposite direction:


JPEG assumes similarities in RGB color planes, correlated with a luminance/chrominance transform for instance. So you choose independent R, G, and B, you are good
8$\times 8$ patches are compressed almost independently, except for the average, predicted for the blocks before (raster order). If you have neighboring blocks with very different means, good
the more the high-frequency, the less a 8$\times$8 block as natural frequency, the better. They avoid long trails of zeros encoded by an EOB symbol.


One cannot easily fulfill all these properties together,  especially with RGB planes made of 8-bit integers. 
Forgetting about the average-thing, generating  independent RGB images, with each pixel randomly $0$ or $255$ (ie high range). Quantization is likely to produced here a lot of false colors. This could give you very bad images for the JPEG in MSE. However, original and compressed ones could look as ugly.

You can find other fractal-based or fancy-patterned proposal in 
What is the least JPG-compressible pattern? (camera shooting piece of cloth, scale/angle/lighting may vary)