I have a moderately gifted kiddo with these deficiencies in Listening comprehension and auditory comprehension(?)/processing(?) constantly coming up (TILLS and TAPS are speech-language assessments):

Neuropsychological evaluation testing that indicate auditory processing/ listening comprehension difficulties:
• KTEA- listening comprehension (score of 84),
• NEPSY2- Auditory Attention (deficient),
• WRAML2- Immediate and Delayed Recall (borderline), and
• California Verbal learning Test (score of 64/Deficient).

TILLS tests that indicate auditory processing/ listening comprehension difficulties:
• Listening Comprehension Subtests – profoundly impaired
• Following Directions Subtests – moderately impaired

TAPS
• Auditory Comprehension – below average (score of 6)
• Auditory FigureGround (Listening Comprehension Supplemental) (score of 7 just one point into average

He has been tested extensively and all it started because his spelling and writing fluency were/are so low. Anyone know what this looks like? How do I treat/remediate this? Could these deficiencies be the root of his spelling and writing difficulties? Or is this a separate issue?

I am lost.

What does this look like? How do we treat/remediate this?

Yes, they could be contributing factors to his spelling/writing fluency issues. How is his auditory working memory/phonological memory? (Might have been assessed on the WRAML or NEPSY additional measures.) It's one of the three key prongs of phonological processing usually considered important in fluent reading/spelling (phonological/phonemic awareness, phonological memory, rapid automatized naming), it's often impaired in dyslexic/dysgraphic learners, and it can present as impairments in any of the areas of listening/auditory comprehension you listed.

There isn't a lot known to be effective at remediating the underlying deficiency, but one can:
1. accommodate/scaffold for comprehension and writing, for example,
a. keep verbal input clear and concise;
b. repeat/rephrase directions;
c. pair visual & verbal;
d. provide clean copy of notes (for higher grades);
e. orally assess for content;
f. oral pre-writing exercises;
g. assistive technology (e.g., speech-to-text, typed response, spellcheck in higher grades or when spelling is not the focus of instruction);
h. additional time; and,

2. accommodate for attention:
a. gain attention prior to giving directions;
b. preferential seating, away from background noise;
c. check frequently for attention and comprehension; and,

3. remediate the end skills in spelling and writing using
a. direct, evidence-based instruction for reading/spelling (e.g., Orton-Gillingham), with a lot of repetition, review, and reinforcement built in;
b. explicit instruction in the writing process and range of typical writing forms, including graphic organizers for the structure and organization of different types of writing.

Ultimately, the hope is for the student to narrow the academic skill gaps, and internalize some compensatory strategies and the self-advocacy skills to request necessary accommodations. Long-term plans, of course.