"Videl jsem je na vlastni oci" sounds more naturaly.
It is a more common idiom (and it is accepted), but "vlastníma očima" is not impossible (24 hits in the corpus, some of them with a slightly different meaning) and it is closer to the topic of this skill.
This sounds like I saw them before my eyes transplant...
See https://goo.gl/ToFjSv
I´m not saying that it is not possible to use it at all. But in this sentence, it sounds unnatural.
Why isn't "Já jsem je vidět vlastníma očima" accepted?
You cannot use the infinitive here, you need the past participle (also called the l-participle).
Thank you, my mistake!