I just recently found out about the flowers having genes. You can find the data here:
https://pastebin.com/c9ZAwpeV.
Tulip Dominance Order
Red
Yellow
Orange
Black
Pink
Purple
White
Blue
Red Tulip Seeds from Lloid are red/yellow
Orange Tulip Seeds from Lloid are orange/white
Tulip Mutations
white/white mutates to black/white 70% of the time
red/white mutates to pink/white 70% of the time
black/pink mutates to purple/blue 70% of the time
EDIT: Failure rates are 10% for all, except 20% for purple.
Pansy Dominance Order
Red, Yellow, Blue (all the same)
Coral
Purple
White
Red Pansy Seeds from Lloid are red/white
Yellow Pansy Seeds from Lloid are yellow/white
Orange Pansy Seeds are red/yellow
Red-Blue Pansy Seeds are red/blue
Yellow-Blue Pansy Seeds are yellow/blue
Pansy Mutations
yellow/yellow mutates to coral/white 70% of the time
coral/coral mutates to blue/white 60% of the time
red/blue mutates to purple/white 30% of the time
EDIT: Failure rates are 10% for all, except 20% for red-blue and yellow-blue.
So if you want blue tulips and someone has one in their garden, you know that the blue tulip is blue/blue. You could breed a Lloid Orange Tulip (orange/white) and all your seeds would be Orange (orange/blue) and White (white/blue). Then, when you cross the new Orange seeds (orange/blue), you'll get half blue/blue and half orange/blue.
My understanding (and it appears to be correct) is that seeds are first in, first out (and I assume the flowers too). If you have 100 Lloid Orange Tulip Seeds (orange/white), then you breed 50 Orange seeds that are orange/blue, you'll have to plant or sell the 50 orange/blue before you can get to the 100 orange/white. EDIT: Sadly, the game doesn't seem to store them this way and it makes it difficult to track several combinations of the same dominant flower color.