Підкладка й рукав чисті.

Й and і both mean and. They are variants of the same conjunction.

In this sentence, й is used mainly for smooth pronunciation:

• Підкладка й рукав sounds a bit easier and more natural than
• Підкладка і рукав

This choice is often about euphony: Ukrainian prefers combinations of sounds that are easier to say. In many cases, і and й are interchangeable, but one may sound better depending on the surrounding sounds.

In the present tense, Ukrainian usually omits the verb to be.

So:

• Підкладка й рукав чисті. literally looks like
• Lining and sleeve clean.

But it means:

• The lining and the sleeve are clean.

This is completely normal in Ukrainian. The present-tense is / are / am is usually not expressed.

Because together they form a compound subject:

• підкладка = the lining
• рукав = the sleeve

Even though each noun is singular, together they mean two things, so the adjective is plural:

• чисті = clean (plural)

Compare:

• Підкладка чиста. = The lining is clean.
• Рукав чистий. = The sleeve is clean.
• Підкладка й рукав чисті. = The lining and the sleeve are clean.

They are in the nominative case, because they are the subject of the sentence.

Forms here:

• підкладка — nominative singular
• рукав — nominative singular
• чисті — nominative plural adjective

So the structure is basically:

• [subject] + [subject] + [predicate adjective]

The genders are:

• підкладка — feminine
• рукав — masculine

So if each noun appeared by itself, the adjective would agree like this:

• Підкладка чиста. — feminine singular
• Рукав чистий. — masculine singular

But when they are combined, the adjective becomes plural:

• Підкладка й рукав чисті.

In the plural, Ukrainian adjectives do not distinguish masculine vs. feminine here, so чисті works for both together.

Here чисті is an adjective used as a predicate adjective.

Its dictionary form is:

• чистий = clean

Some forms are:

• чистий — masculine singular
• чиста — feminine singular
• чисте — neuter singular
• чисті — plural

In this sentence, it describes the subject підкладка й рукав, so it must agree in number.

Yes, Ukrainian word order is fairly flexible.

The neutral order here is:

• Підкладка й рукав чисті.

But other orders are possible for emphasis, for example:

• Чисті підкладка й рукав.

That sounds more marked or stylistic, with extra focus on clean. For a learner, the original order is the safest and most natural.

A rough pronunciation guide for an English speaker:

• Підкладка ≈ pid-KLAD-ka
• й ≈ a short y sound, like the y in yes
• рукав ≈ roo-KAV
• чисті ≈ chys-TEE

A few helpful notes:

• и in чисті is not exactly English ee or ih; it is a central Ukrainian vowel.
• Stress matters:
  • підкла́дка
  • рука́в
  • чисті́

Not always. Рукав can mean:

• sleeve of clothing
• in other contexts, a branch or arm of something, such as a river branch

But in this sentence, especially with підкладка (lining), it clearly means sleeve of a garment.

Підкладка usually means lining — the inner layer of clothing, a bag, a coat, and so on.

So in this sentence, the context is probably something like a coat, jacket, or another garment:

• The lining and the sleeve are clean.

It is a common clothing-related word, and it is feminine:

• ця підкладка = this lining

No, it would not be wrong:

• Підкладка і рукав чисті.

That is grammatically fine. The version with й simply sounds smoother in this particular phrase to many speakers. This is a pronunciation/style choice, not a change of meaning.