Most hedge species produce flowers but they are rarely seen because the trimming of a hedge usually takes place when flower buds would be growing.
If you want to have a hedge that flowers, you will need to be prepared to let the hedge grow naturally and not be tempted to tidy it up with a prune. Leave your hedge to grow until it flowers and if you like the effect, then you can trim and tidy the hedge once the flowering has finished. You must then leave the hedge alone until the same time next year and repeat again.
Some popular flowering hedges are berberis, hawthorn, native mixture, Osmanthus and Photinia ‘Red Robin’