A second Perch of Kairos is blocking the Rainbow Dragon!

Rainbow Dragons are randomly bred from any combination that has at least 4 different elements.

Moon/Sun dragons can only be bred with a combo including cold and lightning. Sun dragons are bred between 7am and 7 pm while moon dragons are bred between 7pm and 7am. No, that's not a rumor. Dragons must be at least level 15 or higher or else this will be very difficult.

Scorch/Cold are popular pairings for both sun and moon.

Your chances are about 10-20% For Flower/Tree according to the wiki and the database. Other combinations seem not to work terribly well aside from clover/flower which seems somewhat promising.

If you don't have a Sakura, then it is nowhere as no such thing as your Sakura even exists.

You haven't gotten a single one likely due to poor luck. You were unclear how many of which of those 2 combinations you tried, but as I said, Flower/Tree seems the more successful. Dragonvale breeding is random. Even with a 99% chance of success, it is possible however unlikely to fail 1 million times and you are not guaranteed of anything.

Rainbow and Sun/Moon have much lower chances (something like 3% maybe as per the other question) so your tale is not uncommon. It's still random so others getting more of them through better luck means nothing to your situation.

There's not really much advice to give on what you are doing wrong as there's nothing wrong being done. The only advice to give when trying to beat a pseudo-random number generator is to keep trying. It's unclear whether the epic breeding island will help, but it might be worth a shot to increase your chances. You could try other combinations though and the ones listed on the database include some information about your chances, but most of the combinations other than Flower/Tree lack enough data to be reliable so try at your own peril.