To unlock the Unicorn and Dragon rideable you must complete all 5 parkour challenges as well as find the 20 gemstones. Once you've found the gemstones, you need to place them on top of the glowstone blocks in the Prize Hub. The parkour challenges will light up green to show you've complete them and the sign to the right of the scavenger hunt will change to "Found: 20/20". Once this is done, two red chests will appear next to the Prizes which contain spawn eggs.
Alternatively, you can type "/gamemode creative" and search the creative inventory for the unicorn and purple dragon spawn eggs.