prog
  彼のバイオリンの音を聞くと歯が浮く｜The sound of his violin sets my teeth on edge .
  彼は歯の浮くような文章の手紙をよこした｜He sent me a letter written in an irritatingly affected style.
  歯の浮くようなお世辞はやめてくれ｜((口)) Don't lay it on so thick.

collins
  If you say that something sets your teeth on edge, you mean that you find it extremely unpleasant or irritating.

〈齒／歯／は／ハ〉が〈浮／う〉く

Google N-gram Corpus Counts
╭─ーーーー─┬───────┬───────╮
│ 歯が浮く │ 8,198 │ 97.8% │
│ 歯がうく │   164 │  2.0% │
│ はがうく │    24 │  0.3% │
├─ーーーー─┼───────┼───────┤
│ 歯が浮い │ 5,188 │ 95.0% │
│ 歯がうい │   252 │  4.6% │
│ はが浮い │    22 │  0.4% │
│ はがうい │     0 │  0.0% │
╰─ーーーー─┴───────┴───────╯

Maybe something like this

@@ -8,0 +9 @@
+<ke_inf>&sK;</ke_inf>
@@ -15,0 +17 @@
+<misc>&id;</misc>
@@ -16,0 +19 @@
+<gloss>to become annoyed</gloss>

GG5 浮く - Sense 3: 〔歯が〕 be on edge; feel loose.

Not sure either is a metaphor. The kokugos don't seem to have these in the same sense of 浮く.
I suspect the use of 気障 (きざ) is just indicating what puts one's teeth on edge.

https://www.jlogos.com/d004/5351237.html

I must point out that this entry is very confusing to a non-native speaker of English, because it is not clear which of these tooth-related glosses is a metaphor and which is literal. Would there be a non-tooth-related gloss available somewhere?

Also worth pointing out that there is the word きざ appearing in most Japanese definitions which is not apparent in this entry.

that's the only sense in gg5, so making the switch

@@ -16,1 +16,1 @@
-<gloss>to get loose teeth</gloss>
+<gloss>to have one's teeth set on edge</gloss>
@@ -21,1 +21,1 @@
-<gloss>to have one's teeth set on edge</gloss>
+<gloss>to get loose teeth</gloss>