empty /release the air ,then ,stick a can of slime in it 
A GOOD tyre fitter would break the bead, clean up the bead area, put some decent bead sealer on ,set it back on the bead, leave it low pressure for an hour, then put it to full pressure .then test it for leaks
NOT a "5 minute ,while you wait job "
Fix
Often
Repair
Daily
A few years ago I had all of the tyres removed and the rims cleaned up to no avail, and every time I have had new tyres I've mentioned the leaky rims and asked them to clean them up, but they still leak

I've got used to checking the pressures regularly, and always check them before a long journey, but getting fed up now so thinking about biting the bullet and having them refurbed, but there's no point if this flat spot can't be fixed.

The flat spot is imperceptible really. About an inch, and the gap between the rim and the ridge on the tyre widens from about 5mm to 8mm, but that's where the biggest leak is.
