"水中月" is a buddhism translation. the 梵漢辭典 has entries:
ambu-candra 水中月
ambu-candraka 水月
in 大智度論 釋初品中四緣義第四十九, there're 3 occurrences of "水中月":
[0297a23] . . . 譬如小兒見水中月﹒心生愛著﹒欲取而不能得﹒心懷憂惱
[0297a28] . . . 如水中月﹒雖為虛誑無所有
[0298a05] . . . 譬如小兒見水中月﹒入水求之﹒不得便愁
this version of 大智度論 is translated by Kumārajīva (鳩摩羅什), at about ad 405.
another one, in 大方廣佛華嚴經 卷第二十五, there're 2 occurrences of "水中月":
[0558b01] . . . 九﹒以幻夢影響水中月故﹒一切法平等
[0561a16]. . . 隨順諸法如幻﹒如夢﹒如水中月不二相﹒而起分別種種煩惱及不失業果報
this version of 華嚴經 is translated by buddhabhadra (佛馱跋陀羅), at about ad 412
about 鏡中花, imo, it's an "inspired" term, derived from "ādarśa-maṇḍala-pratibhāsa" (鏡像).
in 大智度論 大智度初品中十喻釋論第十一, there're several occurrences of "鏡中像":
[0101c08] 解了諸法如幻﹒如焰﹒如水中月﹒如虛空﹒如響﹒如犍闥婆城﹒如夢﹒如影﹒如鏡中像﹒如化
[0104c07] . . . 如小兒見鏡中像﹒心樂愛著﹒愛著失已﹒破鏡求索﹒智人笑之
[0104c26] . . . 諸法從因緣生﹒無自性﹒如鏡中像
"鏡中花" as a term, the earliest one i find is in poem "徐州送丘侍御之越" by 皇甫冉, of 唐 dynasty:
時鳥催春色﹒離人惜歳華﹒遠山隨擁傳﹒芳草引還家﹒北固潮當濶﹒西陵路稍斜﹒縱令寒食過﹒猶有鏡中花
my guess (might be wrong, need evidence to prove) is: zen monks in 唐 dynasty used "鏡中花", instead of "鏡中像" (the correct, original term); pair with "水中月", to talk about buddhism.
"花" & "月" (flower & moon) is a perfect match :) better than "像" & "月"
tired now, have fun :)