Yes. It is a fact admitted in main Sunni books that Umar ibn al-Khattab ran away from Uhud and Hunain and Khaibar.
1. Saheeh Al-Bukhari; Hadeeth number 3978 which is very clear that Umar b. Khattab ran away from the battle of Hunain with those who ran away.
2. Saheeh Al-Bukhari, V.5, P.101.
3. Fat-h Al-Bari Fi Shar-h Saheeh Al-Bukhari by Ibn Hajar, V.8, P. 29.
4. Omdatul Qari Fi Shar-h Saheeh Al-Bukhari, V.17, P. 299 .
5. 'Awn Al-Ma'bood , V.7, P. 275.
6. Al-Budayah Wal-Nihayah by Ibn Katheer.
7. Al-Seerah al-Nabawiyyah by Ibn Katheer , V.4, P. 264 and V. 2, P. 89 and V.3, P. 51.
8. Seerat Ibn Hisham, V.2, V. 415.
9. Soyouti in al-Dorr al-Manthour , V. 2, V. 88 narrated from Umar himself how he ran away from the battle of Uhud.
10. Al-Tabari in his Tafseer, V.4, P. 193 narrated from Umar how he ran away from the battle of Uhud and climbed the mountain running like a goat.
11. Kanzul Ummal by al-Muttaqi al-Hindi, V. 2, P. 376.
12. Great Sunni books of Tafseer like Al-Fakhr al-Razi (9:51) mentioned this fact.
13. Ibn Asakir in Tareekh Dimashq , V.24, P. 396.
14. Al-Hamawi in Mo'jam al-Boldan , V.4, P. 173.
15. Al-Salihi al-Shami in Sobol al-Huda , V.4, P. 206.
16. Al-Waqidi as narrated by Ibn Abi al-Hadeed, V. 15, P. 22.
17. Al-Haakim al-Nisabouri in al-Mustadrak 'ALAL-Saheehain, V.3, P. 40.
18. Al-Mussannaf by Ibn Abi Shaibah, V.7, P. 396.
19. Al-Albani Nasser , the well known Wahabi Shaikh in his book Erwaa' al-Ghaleel, V.5, P. 53.
20. Majma' al-Zawaa'id by al Haithami, V.6, P. 136.