The Messenger of Allah ﷺ permitted silk to the width of two fingers.
حدثنا خلف بن الوليد حدثنا خالد عن خالد عن أبي عثمان
أن رسول الله ﷺ رخص في الحرير في إصبعين
No references are available.
Its isnad is sahih. Khalid is Ibn Abdullah bin Abdul-Rahman Tahhan. From Khalid, that is Ibn Mihran Hadhdha. From Abu Uthman, that is Nahdi. The hadith is an abridgment of 92, and see also 123 and 181.