When speaking Japanese, how can one discern between Kanji and kana?

The scripts don't matter for the spoken language.

You are talking about homophones or determining where a word ends and begins. All languages have that issue to some degree.

English: where, wear, aware (all have the "ware" syllable). sea, see, mercy (all have the "see" syllable). one, won. to, too, two. its, it's. sail; sale; for, four; ate, eight; hear, here. pair, pear, pare, repair etc. English has tons of these. Context makes it clear.

It's the same in Japanese.

Often homophones function as different parts of speech, which makes the differences beyond easy. When they are in the same word class, it's usually clear which meaning is intended. If not, a synonym can be used or the listener can ask a question.

Kana is just phonetic writing. Any kanji can be written in kana.

As far as homophones go in Japanese, it's pretty much all context and usage. No Japanese person would mistake something like 日(day) and 火 (fire) even though both can be pronounced "hi". English isn't exactly stranger to homophones either.