From my experience of cleaning photo lenses (doing that for almost 40 years on Carl Zeiss, Nikon and Fujifilm lenses) right now there are two excellent solutions for that:
Lens Clean from VisibleDust:
https://visibledust.com/products3.php?pid=304
it's non-alcohol solution. Can be shipped from overseas. Doesn't leave any streaks. Available on Amazon/eBay/B&H etc.
Eclipse Optic Cleaning Solution:
https://www.bhphotovideo.com/c/produ..._Cleaning.html
Unfortunately cannot be shipped by air. There was a local source of this solution in Australia, but looks like it's gone recently.
Lens Clean from VisibleDust is probably the easiest to get, cheap and works exceptionally well on multicoated optics.
In terms of cloth/fabric - yes, microfibre cloth is the way to go, but just make sure you've got lint free one, made specifically for optics.