In like the grand prix jumpers are they aloud to where like designs on there hunt jackets like flowers ec...?

They can wear whatever they want but it's disrespectful. I have see riders wearing orange and lime green jackets, they are not going to get booted out of the ring. Most grand prix competitions honor someone such as the owners, sponsors, etc.... It's respectful to wear the white breeches, and a simple colored jacket such as black, navy, red, or hunter green. Occasionally they are allowed to wear raincoats. Some shows host themed puissance where the riders can dress up. Most commonly in a regular competition they wear plain jackets.