Mid summer is the best time in the UK to minimize the risk of silverleaf infection - but I don't know whether that might make your tree vulnerable to something where you are that we don't have here.

Introducing an infection by pruning is exactly what I was worrying about Bamboo. I do have to prune since all of the branches are touching and I do want to get some clearance from the ground. Going by what you say I will prune mid July and I'll make a bleach solution to dip the tool in so as to disinfect it as I go along. Thank you my friend.

I had just come here to ask the same question LOL
Well! No need to ask now as Bamboo has answered it already LOL but someone said after it has flowered too?

Well, mid summer is after its flowered - well after... There are many shrubs where immediately after flowering is absolutely the time to prune, but flowering cherry isn't one of them because of the silverleaf risk. You may lose some flowers though, because it isn't usual to prune ornamental cherries anyway - unless the circumstances are like Loosestrife mentions, when you might remove anything touching the ground, but not massively prune the whole thing.

Thanks Bamboo x