The method is valid but you need to go big for two reasons:
Firstly, and obviously those two reds together at the end only have a 1.6% chance of producing a blue flower (when they breed).
Second is not shown on the picture. The orange and purple breed in the final step can produce four different flowers. Two of them are white and two of them are red. They might look the same but because of genes two two reds are not identical. And only one of the two can make blues when bred with itself. The other red is useless. And the issue... you have no way to tell them apart.
Because of the second point you need to churn out lots of these reds. Normally I’d say clone after you have one of what you need and scrap the breeding pairs. But because you don’t know what’s good or bad here you just have to keep spawning more reds from the orange/purple combo.
You also want to plant in blocks not specific pairs (basically you want just enough spaces for new flowers to spawn into). This way different pairs breed each night so you’re mixing up and hoping a good pair breed. You might also consider moving the flowers around occasionally to mix them up again.
Your big block of reds is going to spawn more reds. These should be mixed back into your planting as some of these reds can make blues too (but not all).