Garden themes

Using common names you may use red vinca and white vinca. For blue you can use blue impatiens or blue petunias. They are easily obtainable and are in flower from late spring till the end of summer so there will be plenty of time for everyone to enjoy them.

Great idea, not just for the Queen's birthday, but they combination is striking - and patriotic.
Depends if you were looking for annuals or perennials. Annuals could be blue and white bush lobelias, red Salvias, white/red Antirrhinum - mind has gone blank on other blues at the moment!
Bizzie Lizzies come in reds as do Begonia's but you could always wait until the frost has passed and have a look at the bedding plants for colours. Don't forget that lobelias come in a variety of blues, you need the dark one.

Thanks for the idea, the both of you. For our Independence Day (USA) I always hung out our American flag and bunting. This year I will raise the floral colors.