I don't see a problem so long as you can keep your courgette plant from sprawling all over the flower bed.

The ornamental kitchen garden idea is a lovely one, but the trouble is that most flowers and vegetables like entirely different conditions. For example, vegetables, especially courgettes, like deep, moist well tilled soil with lots of nutrients and compost, while many flowers do better in dry soil with minimal nutrients. Many types of flower do well in shade, but most vegetables want lots of light and sunshine.
So your courgette may not do very well in this position, especially only a foot from a strong growing dominant plant like a red hot poker.
All you can do is make a deep planting hole for the courgette and fill it with lots of rich compost, and keep it well watered. I suspect it WILL swamp the surrounding flowers though, and it's difficult to cut courgettes back as new fruit are borne on the new growth as it spreads out.

To take Mg's and Bertie's comments further you could do as I do and plant them in bottomless pots, roughly 10" (250mm)in diameter.

These you could fill with a humus rich soil ( Bertie's comment) but what you must bear in mind is Mg's comment, they need quite a lot of space circa one metre in diameter minimum.

Just another comments pick the courgettes very young (4"-6" long) for two reasons;

1) they taste better
2) it encourages more fruit

If you allow them to remain on the plant they will grow to marrow size which in my opinion taste "more watery" and you get less fruit!