I thought that Kurdish was written with the Arabic script. But then many Kurds live in Turkey, and there they may be legally required to use the Latin script for their language like the Turks.

Looking at Omniglot, their illustration shows ẍ beside its equivalent, Xh, in an alternate Latin script for their language, and beside the Arabic and Cyrillic script equivalents. I would take that as sufficient evidence that ẍ corresponds to an actual element of Kurdish phonology and orthography. On the other hand, ḧ is not shown on the Omniglot page my Google search turned up. (Oh, wait, it did appear once - in the chart of how Kurdish can be written with the Armenian script.)

The Wikipedia article on Kurdish Alphabets does give detail. It turns out that the two letters you mention, plus the apostrophe, were part of Jeladet Ali Bedirkhan's original proposal of a Latin alphabet for the Kurdish language, but only for rendering words of foreign origin, as the sounds they represent are not native to Kurdish. Old orthography Russian had extra letters for words borrowed from Greek, and Tibetan and other Indic scripts have extra letters for writing Sanskrit, so this isn't that unusual - for that matter, in French, the letter W has that status.

On top of that, until very recently, since the letters Q, W and X aren't part of the Turkish language, Turkish law forbade Kurds from using them.

This article is another source for information on Kurdish scripts, but it doesn't mention those letters at all.

Check out what the Kurds do on their web page, e.g.

http://cabinet.gov.krd/?l=16

Given what is said in http://de.wikipedia.org/wiki/Ḧ and http://de.wikipedia.org/wiki/Ẍ, a combining diaeresis U+0308 that is well positioned might be enough.

PS The French Wiki provides the additional information that those letters are found in the ALA-LC-romamization of Kurdish. Cf http://www.loc.gov/catdir/cpso/romanization/kurdish.pdf When searching Wikipedia, it is good to check what is said about your search in various languages.

I cannot spot any occurences of the characters in question on that site.

OK. It seems that those ch.s are real exotic ones.
Thanks for your hints!