What type of paint can I use for exterior flagstone?
In Dallas TX people are painting perfectly good brick because they think it is a design choice. I personally would never paint perfectly good brick.

In my neighborhood of brick facade homes I have, however, seen one case I personally thought it sorta worked. A house with uniform bright red brick with off-white tooled mortar was painted with a highly diluted white latex paint. The owners described it as a "wash".

It desaturated the red and gave some variation which was interesting. If you tried that on your flagstone, wear patterns would probably develop, but maybe you could periodically "rewash" those areas. And if it didn't work at all, you might be able to remove it with a power washer. If you have an inconspicuous place, you could test this.

Personally, I would try to live with the bold flags, and try to consider them a fact of nature which is too much trouble to change by art.