I get the same flies in my garden for about 7-10 days in the spring. Ruled out manure around the roses, dog poo and slugs this year. They all congregate near to an east-facing garage wall which gets very warm.
The only time I got shiny bluey green flies was when I spread "soil conditioner" on the garden. I bought this stuff from the GC but I think it was council green waste bagged up for commercial sale. I avoid soil conditioner now.
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You’ve possibly poisoned your dogs !?!?!
I think you should be checking with your vet as a matter of some urgency ... have the packet the slug pellets were in with you when you phone.
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.