What is the origin in a strong Scouse accent of the phoneme /x/ or sometimes /kx/?

This is a common phonological process known as lenition. For this to occur in a dialect of English, one does not require contact with or influence from another language.

Allophonic variation between [k] and [x] is something that can easily spring up naturally. Both /k/ and /x/ are articulated in the same place in the mouth and both are voiceless; the only difference between the two sounds is that /k/ is a stop (or plosive), while /x/ is a fricative. So, the relationship between /k/ and /x/ is analogous to that of /t/ and /s/, or /p/ and /f/.

When you articulate a stop, you bring your tongue to the roof of your mouth and make a full closure. When you articulate a fricative, you only make a partial closure, such that the small space causes frication. So the lenition path (stop to fricative) is simply an "opening" of the sound, i.e. an early relaxing of the tongue.

In Standard English, (basically) anytime the /k/ sound is made, a full closure is maintained during the entire consonant. In Scouse, when you get [kx], an affricate, the speaker makes a full closure for only part of the time (the [k]) but allows the tongue to open more during the latter half of the consonant sound (the [x]). When the sound is only [x], the speaker never quite makes the full closure — so this is an even further progression of the lenition process.

Lenition over time is one way that a consonant can gradually change into a completely different sound. So, for example, the biggest difference between Spanish estudiar and French étudier is the lack of /s/ in French; this "s" used to be present, but was lost through diachronic lenition (— Argentinian Spanish is beginning to lose their /s/ through lenition as well — turning it into [h] for the time being).