(According to web searches,) there is a distinction called 意志動詞 and 無意志動詞. The former denotes the verbs that express voluntary actions.
The rule is that there is no potential form for 無意志動詞, which 合う in 気が合う belongs to.
For comparison, 分かり合う is a voluntary action, so 分かり合える is fine.
(Another confusing element may be the English "get along", which may well be understood as a voluntary action.)
Another example may be instructive (partially from the link above).
- 医者になる → 医者になれる
- 春になる →
To be a doctor is something one does at her own will, but the coming of spring is not. Hence the difference.