die Spülung
flush
The device on a toilet that directs water into the bowl to wash away its contents.
Die Spülung an unserer Toilette ist kaputt und läuft ununterbrochen.
The flush on our toilet is broken and keeps running continuously.

flush / conditioner / rinse
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flush
The device on a toilet that directs water into the bowl to wash away its contents.
Die Spülung an unserer Toilette ist kaputt und läuft ununterbrochen.
The flush on our toilet is broken and keeps running continuously.

All meanings of 'die Spülung' derive from the verb 'spülen' (to rinse/flush), which means 'to clean something with a liquid or let a liquid flow through it.' This basic idea of rinsing or flushing connects the toilet flush, hair conditioner, and medical irrigation.
Kannst du bitte das Gemüse kurz spülen?
Can you please rinse the vegetables briefly?
The context makes clear which meaning is intended. Words like 'Toilette' (toilet) or 'WC' point to the toilet flush. With 'Haare' (hair) or 'Shampoo' (shampoo), it is about hair care. In a medical context, words like 'Wunde' (wound) or 'Arzt' (doctor) point to medical irrigation.
Meine Haare sind nach der neuen Spülung viel weicher.
My hair is much softer after the new conditioner.
When talking about the toilet, typical verbs are 'die Spülung betätigen' (to operate the flush) or 'die Spülung drücken' (to press the flush button). Colloquially, you also hear 'die Spülung ziehen' (to pull the flush), which comes from older toilet models.
Bitte nach der Benutzung die Spülung betätigen.
Please flush after use.
In the context of hair care, 'Spülung' (conditioner) is often combined with verbs such as 'verwenden' (to use), 'auftragen' (to apply), 'einwirken lassen' (to leave on), and 'ausspülen' (to rinse out).
Lass die Spülung ein paar Minuten einwirken, bevor du sie ausspülst.
Leave the conditioner on for a few minutes before rinsing it out.
cleaning
'die Reinigung' and 'die Spülung' can both mean that something is being cleaned. 'Reinigung' is more general: you can clean with water, a cloth, a brush, cleaning agents, or also in a technical process. 'Spülung' means more specifically that a liquid runs through something or is poured over something in order to remove residue. That is why 'Spülung' is especially suitable for pipes, devices, or also in medicine. If the method is not important, 'Reinigung' sounds more natural.

Nach der Reparatur machte der Techniker eine Spülung der Leitung.
After the repair, the technician flushed the pipe.
Die Reinigung der Fenster dauert heute länger als geplant.
Cleaning the windows is taking longer than planned today.