[pooncophy]

There are a few hadeeth in the Sunni books which allude that Abu Bakr has burned hadeeth OR that he prevented hadeeth from being written, but they are all da`eef (weak) per Sunni `ilm al-hadeeth.

عن عائشة أنَّها قالت: «جَمَع أبي الحديث عن رسول الله (ص) وكانت خمسمائة حديث، فبات ليلته يتقلّب كثيراً. قالت: فغمّني، فقلت: أتتقلّب لشكوى أو لشيء بَلَغك؟ فلمّا أصبح قال: أي بُنيّة، هَلُمِّي الاَحاديث التي عندك. فجئته بها، فدعا بنار فحرقها. فقلت: لِمَ أحرقتها؟ قال: خشيت أن أموت وهي عندي فيكون فيها أحاديث عن رجل قد ائتمنتُه ووثقتُ [به]، ولم يكن كما حدّثني فأكون نقلت ذلك»
From `Aa`ishah said: "My father collected the hadeeth from the Messenger of Allaah , which was five hundred hadeeth. He spent that night so sleeplessly and restlessly that I was sad for him." I said: "Are you moving restlessly due to an ailment or information that you received?" When it was morning, he said: My daughter, he asked me to fetch him the collection of Hadith that he had put with me. When I fetched them, he set fire to them. As I asked for the reason, he replied, 'I anticipated that I would die while I still have this collection among which there might be reports of a man that I deemed trustworthy while he was the opposite; therefore, I would be the narrator of such false reports.'
Source:

• al-Dhahabi, Tadhkirah al-Huffaadh (Beirut, Daar al-Ihyaa' al-Turaath, n.d) , vol. 1, pg. 5
  Grading:
• al-Dhahabi said "This hadeeth is no saheeh" (فهذا لا يصح)

ومن مراسيل ابن أبي مليكة ان الصديق جمع الناس بعد وفاة نبيهم فقال إنكم تحدثون عن رسول الله صلى الله عليه وسلم أحاديث تختلفون فيها والناس بعدكم أشد اختلافا فلا تحدثوا عن رسول الله شيئا فمن سألكم فقولوا بيننا وبينكم كتاب الله فاستحلوا حلاله وحرموا حرامه .
And from a mursal of Ibn Abee Maleeah that al-Sideeq gathered people after the death of their Prophet and said, 'You are reporting about the Messenger of Allah inconsistent narrations. People coming after you will be engaged in more intense discrepancy. Therefore, do not report anything about the Messenger of Allah, and if anyone asks you, you should refer to the Book of Allah as the arbitrator. You should thus deem lawful whatever is lawful therein and deem unlawful whatever is unlawful therein.
Source:

• al-Dhahabi, Tadhkirah al-Huffaadh (Beirut, Daar al-Ihyaa' al-Turaath, n.d) , vol. 1, pg. 2-3
  Grading:
• al-Dhahabi said "Mursal" (فهذا المرسل)