The Prophet (ﷺ) allowed `Abdur-Rahman bin `Auf and Az-Zubair to wear silken shirts because they had a skin disease causing itching.
Sahih al-Bukhari Book 56, Hadith 132
← Previous Hadith Allah's Messenger (ﷺ) went out to answer the call of nature and on his return I brought some water to him. He performed the ablution while he was wearing a Sha'mi cloak. He rinsed his mouth and washed his nose by putting water in it and then blowing it out, and washed his face. Then he tried to take out his hands through his sleeves but they were tight, so he took them out from underneath, washed them and passed wet hands over his head and over his leather socks.

Sahih al-Bukhari Book 56, Hadith 131 Next Hadith → As above. Narrated Anas:

`Abdur Rahman bin `Auf and Az-Zubair complained to the Prophet, i.e. about the lice (that caused itching) so he allowed them to wear silken clothes. I saw them wearing such clothes in a holy battle.

Sahih al-Bukhari Book 56, Hadith 133