We would say neither:
「この花は水をやられた。」
nor
「この花は水がやられた。」
for two reasons. These "sentences" sound far more unnatural and awkward to native speakers than you could probably imagine.
Reason 1:
While the "grammatical" passive-voice form of 「やる」 is certainly 「やられる」, the latter generally has a fairly negative connotation. "To have something undesirable done (to you)" is the usual meaning/nuance of 「やられる」.
Reason 2:
Inanimate subject -- 「この花」. It is not nearly as common in Japanese as it is in English. Japanese-learners tend to use the inanimate subject in Japanese because they tend to translate directly from their native languages.
Thus, while "This flower was watered." is a perfectly natural English sentence, its literal counterpart 「この花は水をやられた。」 is not a sentence native Japanese-speakers would ever form under normal circumstances. It is that off. It sounds as if it were a big mistake to water that particular plant.
So, how would we say "This flower was watered."? I would use the unmentioned "I" and say:
「この花には(もう)水がやってある。」 or
「この花には(もう)水をやりました。」
Notice both are in active-voice. The passive-voice simply would not work here unless you wanted a stiff, wordy and unnatural sentence like:
「この花はすでに水を与{あた}えられています。」
You would sound like a robot (or Google Translate) if you said that.
A brief explanation of the use of が in passive phrases would also be appreciated.
This is what I take you to be talking about.
「Aは + Bが + [passive-voice verb]」
means:
"As for A, B has been ~~." ← B is part of A.
You can say things like:
「私は肝臓{かんぞう}がやられている。」 = "As for me, my liver is damaged."
↑ That is how you use 「やられる」.
「Aさんの家は、台風{たいふう}で屋根{やね}が吹{ふ}き飛{と}ばされてしまった。」 = "As for A's house, its roof has been blown off by the typhoon."