Two schools of thought on that one.
Pinching out the flowers will stop the the plant putting it's energy into seed production so you get larger tubers to harvest.
Not pinching out the flowers saves lots of time and effort relative to the difference it makes to the size of the tubers you harvest.
I've not really seen any actual evidence to support either theory - maybe pinch out the flowers on one row and not on the next, then compare the yields?
Until someone can show the difference it makes, it's up to you which you do.

I don't know if it makes a difference or not, but I have never taken the flowers off our potatoes.

Bob Flowerdew on GQT says it DOES make a difference, but only on lates or main crop. With earlies, the plants tend to die down quickly anyway without setting fruits. Why don't you pinch out all the flowers on one row, and not on the other, and measure the difference in yield?

I have never pinched the flowers off my potatoes but I guess that's because my dad never did it! I think the difference must not be very much because I have never seen a farmer do it either! They are quite lovely purple and/or white flowers that I enjoy looking at and think they make a contribution to the garden.

Agree with that, Ian.

Thank you for all the comments. I think I'll just leave them on, as I agree that I'd like to see the flowers add to the garden, and Ian's comments about farmers just says it all really.