Nasturtiums do fine and come up year after year in a tunnel. Another flower I love in there is scented nicotiana - the non scented type are a waste of space, but the scented ones give off the most glorious smell which fills the tunnel in the evenings. They take up a bit of room but are worth it. If you choose your flowers to be single and fertile ie not sterile hybrids, you will be attracting bees, hoverflies and so on in to pollinate your beans etc.
I always plant tagetes rather than French Marigolds as their smell is supposed to deter white fly - I don't have any white fly, but whether that's because of the tagetes or not I don't know.
It's lovely to have flowers in with your veggies in the tunnel, creating a wonderful jungle.
I did once grow sweet peas in with the climbing beans but they just attracted moulds rather than insects.
I also have various bulbs growing, esp daffodils, by accident as their spot outdoors wasn't quite ready so I popped them in the tunnel and they have been there ever since. The daffodils come into flower early and give me a taste of spring before it has actually arrived.
Go for it - if it doesn't work, pull them out.
Herbs will all do well in the tunnel - plant the heat-loving ones on the south side so they get plenty of sun.