I know there are a few common rules to keep in mind

You're thinking like a modern person. We're used to very fixed rules about how we write. Runes were written from right to left or right to left. There were no consistent conventions for punctuation of spacing. Often, a letter would not be repeated, for example 'don't tase me bro' might be written something like 'dontasemebro', which is what you were referring to as the same symbol never appearing twice in a row. In some instances, we find bind runes where two letters have been written on top of each other or combined in some way. In the Younger Futhark, voiced consonants were not usually distinguished, so b and p would be written with the same rune. Of course, we see these trends, but there are always exceptions, and simply because someone could write runes didn't mean they were very literate. Many inscriptions are gibberish, as if the inscriber had just learned a few shapes and carved them into something because they thought it looked cool or had some sort of magical property.

My background is in Old English and Gothic, so I'm not sure how to deal with the rr at the end of Kjárr. Old Norse final -r is usually a nominative ending that comes from Proto-Germanic -az. This would be written with the rune ᛦ rather than the regular r, ᚱ. Wikipedia gives καισαρ → kaisar → *kēsar → Kíarr → Kiárr, so if we take the name as derived from kēsar + PGmc. -az, we might end up with the Younger Futhark ᚴᛃᚬᚱᛦ.

I'd be much more comfortable putting it into the Elder Futhark, left to right, as earlier ᚲᚨᛁᛊᚨᚱᚨᛉ or ᚲᛖᛊᚨᚱᚨᛉ, then maybe later ᚲᛃᚨᚱᚨᛉ or ᚲᛃᚨᚱᛉ.