Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce kingdom as KIHNG-duhm (/ˈkɪŋdəm/). Stress falls on the first syllable — keep everything else short and quick.
Record yourself saying "kingdom" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
The schwa before M disappears — M becomes the vowel of the syllable. Go straight from the previous consonant to M.

The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the first syllable, not the others. Stretch KIHNG — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.