Red+Yellow in a checkerboard pattern (I prefer tulips, but you can use anything really)
Black+White in diagonals
Orange+Blue in diagonals or check
Anything + Black or White in horizontal stripes
Maybe you could put a strip of white followed red followed by orange, followed by yellow and so on to create a rainbow effect?
Not really an expert, just some ideas
Pink and blue roses
Blue cosmos and blue roses (especially around water/fountains)
Pink roses and white roses
Red or pink carnations with white roses
Pink roses and white carnations
Pink tulips and pink roses/carnations
Pink lilies and white roses/carnations
Jacob ladders and white carnations
Jacob ladders and pink roses/carnations
Gold roses and blue roses
White lilies and pink roses
And all flower hybrids in diagonals going in ROY G BIV (rainbow) order
When I first started my game four months ago, I put flowers around all the villager houses, not really random, but kinda random, knowing I would get back to them after a lot of other landscaping was finished. I started looking at them recently and discovered that gold roses and yellow tulips look stunning together, imo.
Also, around my double hot springs, I have only blue violets and white lilies. They look incredible together, too, imo, epecially with my star path.
White Lilies + Red Tulips
Pink Cosmos + Orange Pansies
Yellow Tulips + Blue Roses
White Carnations + Jacob's Ladders
Red Roses + Black Roses + Gold Roses
White Carnations + Black Lilies