Looking at Kirk's sleeve, we don't see what we would expect from the pattern of the Royal Navy or the United States Navy.
Nor should we. This is Starfleet, after all. There's no reason their rank stripes should have to be the same as real navies. They're different. Let it go.
Besides, we know the stripes used by all ranks below Captain, and they follow a standard pattern: each successive rank adds a half-stripe to the one below it. For example: Lieutenant Commander = one and one half stripes. Commander = two full stripes. Therefore, Captain = two and a half.