Leave the flowers. They are attractive and do not affect the quality of the plant.

FataMorgana

You can eat those flowers. And they attract bees to the garden - very handy when you want pollination of your fruit and veges!

Thanks fatamorgana and daisy.

It is best to harvest thyme when in flower.
Thyme dries easy and keeps the aroma and flavor fo a long time.
If I were you I would harvest and make some winter supply.

I have heard that the best time to harvest thyme is when it flowers.