What sort of reading testing does his school do at the kindergarten level? In the second semester of kinder at my child's school they do the dibels test, which includes a part where the child has to read nonsense words.
Everything that you mentioned, except the slow writing are perfectly normal for a child his age/grade. Spelling "sick" as "sik" is phonetic, and exactly what you would expect from a kinder to first grade child. The fact that he is gifted does complicate things, as what it normal for an average ability child is may not be normal for a gifted child.
Personally, I wouldn't do outside testing at this point, especially since you mentioned that he is reading at a second grade level. Since he is highly gifted, you might expect his reading level to be even higher, but that is high enough in my mind so as not to be a red flag.
I would wait until first grade when they tend to do more reading assessments at school and begin spelling tests. If he struggles in spelling/reading at that point, I would take him for additional testing. I was diagnosed in first grade with dyslexia, and that was still early enough to be successfully remediated for the most severe/limiting issues that dyslexic people encounter. I can read very well, even compared to people without dyslexia, but have below average spelling ability.
My son is ID'd as gifted (though not so much in reading, his strength is math/nonverbal) and he was not a good reader in kinder. He couldn't even blend three letter words until January of kinder year, and that was after I worked with him on it. I was concerned that he might be dyslexic at that point, especially given his genetics (both my father and I are dyslexic). He also had letter reversals, though so did around half of the class. His writing was otherwise unremarkable, though as I recall in kinder they are writing such things as "I see the dog.", I'm not sure how much you can pick up from that.
Now he is in third grade and he reads above grade level and recently placed at a district spelling competition. His spelling ability will likely eclipse mine in the next year or two. He is obviously not dyslexic even though it looked very possible in kinder.
