The Amlicites are often held to be identical with the Amalekites. If they are the same, as seems likely, it would seem unlikely for this alteration in spelling to be rooted in Hebrew, because, an 's' sound, as is found in Amlicite, is not at all connected, in Hebrew phonology, with a 'k' sound. In English, we have a 'c' which connects these two phonemes together and allows for the two sounds to be confused.
Benjamin McMurtry has argued that the groups are distinct, and I believe the points he makes about the timeline are particularly string.