With a nylon or brass/copper bristle bore brush, you should be all right with a 270 (.277) bore brush in a 6.5 mm (.264) bore. Just be careful with the "mops" and wrapping a patch around the bore brush and also using the spiral "Tornado" type bore brushes. Most of all, use a good diameter rod, such as those designed for a .25 or .243 calibre bore, rather than one of the "universal" aluminum rods designed for everything from 17 calibre up to 270. These smaller rods do not lend enough support to give a good push or pull when they are greatly undersized.
It is usually best to clean firearms from the chamber end, rather than from the muzzle, as cleaning rods tend to wear the rifling away at the muzzle over time because they can not ordinarily be pushed or pulled down the bore straight. Be especially careful in putting too much patch material on the jag or slotted end of the rod as you can stick it in the bore.
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