All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Al-Baraa’ ibn ‘Aazib narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said to him: “Whenever you go to bed, perform wudhoo’ like you would for the prayer, lie on your right side and say, Allaahumma aslamtu wajhi ilayk, wa fawwadhtu amri ilayk, wa alja'tu thahri ilayk, raghbatan wa rahbatan ilayk. La malja'a wa la manja minka illa ilayk. Aamantu bi-kitaabika allathi anzalta wa bi-nabiyyika allathi arsalt (O Allaah! I surrender to You and entrust all my affairs to You and depend upon You for Your Blessings, with desire and fear of You. There is no fleeing from You, and there is no place of protection and safety except with You, I believe in Your Book which You have revealed and in Your Prophet whom You have sent). Then, if you die on that very night, you will die with true faith.’ I repeated them to memorize them and when I reached ‘Aamantu bikitabika allathi anzalta’ I said, ‘Wa-bi-rasulika allathi arsalt (your Messenger whom You have sent).’ The Prophet, sallallaahu ‘alayhi wa sallam, said: ‘No, (say): Aamantu bi-nabiyyika-llathi arsalt (Your Prophet whom You have sent), instead.” [Al-Bukhari and Muslim]
He, sallallaahu ‘alayhi wa sallam, would repeat a supplication until the Companions memorized it. Khaalid ibn Ma‘daan narrated: “We were invited to a meal by ‘Abd Al-A‘la ibn Hilaal; when we finished our meal, Abu Umaamah stood up and said, ‘I am not eloquent enough to deliver a speech, nor is it my intention in standing here; but I heard the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, say after eating a meal, ‘Al-hamdu Lillaahi hamdan katheeran tayyiban mubaarakan feehi ghayra makfiyyin wa laa muwadda‘in wa laa mustaghnan ‘anhu (Much, good, blessed praise to Allaah, not sufficed, and not ignored, and not to go without).’ He kept repeating them until we learned them by heart.” [Ahmad]
Ibn Mas‘ood said, “The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, taught me the Tashahhud taking my hand between his, in the same way as he taught me a chapter of the Quran.” [Al-Bukhari and Muslim]
Shaykh Ibn ‘Uthaymeen said that there is no harm in reciting the supplications collectively during the Tawaaf if done for the purpose of teaching and not so loud as to disturb other pilgrims. He said, “Reciting supplications in congregation during Tawaaf has not been reported by the early Muslim generations as far as we know. This is because it disturbs other pilgrims and distracts those who recite supplications individually, especially if the person reciting to the group has a loud voice. However, if he recites the supplications in a low voice to teach his group, then I hope that there is no harm in that.”
Hence, repeating Athkaar or supplications after another person for the purpose of learning is harmless and it is not considered a Bid‘ah. You can also read the supplications from a book or mobile device, for instance.
Allaah Knows best.