Libjstl

We 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 strange and incorrect 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 directly translate from their native languages.

Thus, while "This flower was watered." is a perfectly natural English sentence, 「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. Direct translation is dangerous between two unrelated languages.

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 want an awkward, wordy and unnatural sentence like:

「この花はすでに水を与えられています。」

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."

「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."

You should say この花には水がやってある or この花は水がやってある.
But この花は水をやられた and この花は水がやられた may be grammatically correct.
この花は水がやられた may sound like another flower may be poured a kind of liquid apart from water to.

私は腕を掴まれた。
私は腕が掴まれた。

Both mean “My arm was caught.” But second one sounds like Another one’s leg or hand may have been caught.