As I understood it, angels have no free will and strictly do those things G-d instructs them to do. But in the brachas preceding krias Shema, we say that the angels "all accept upon themselves the yoke of heavenly sovereignty from one another, and grant permission to one another to sanctify the One Who formed them . . . ." If an angel has no free will, what power does it have to grant permission to another angel to do anything? Isn't it G-d that gives them whatever authority they have?
After searching around, I found something that somewhat contradicts what I said in my earlier comment where I suggested that r'shut simply means "making space," that is, non-interference. It seems that there is an understanding that r'shut actually does mean giving permission, but the permission seems to have been ordained from a source higher than regular angels -- either a very top tier angel or actually from Hashem.
I found a discussion of this on the website Beurei Ha-Tefila compiled by Abe Katz: http://beureihatefila.com/files/Reconciling_the_Multiple_Themes_of_Yotzer_Ohr.pdf
There, he mentions a source in Mesechet Chullin 92b. The relevent text begins with these words: "And the angel said: (Breishit 35) Let me go, for the day breaks. Jacob said to him, ‘Are you a thief or a rogue that you are afraid of the morning?’ He replied: ‘I am an angel, and from the day that I was created my time to sing praises to the Lord had not come until now’. This supports the statement of R. Hananel in the name of Rab. For R. Hananel said in the name of Rab: Three divisions of ministering angels sing praises to the Lord daily; one proclaims: Holy, the other proclaims: Holy, and the third proclaims: Holy is the Lord of hosts."
The discussion in Chullin goes on for some time and talks about how angels cannot perform their praises until they have permission to do so. The angels are organised into legions and types, and each type of angel must wait its turn before it can begin to sing. (There is also an issue of all angels having to wait until B'nei Yisrael sing their praises, but that's another matter.)
On the same Beurei Ha-Tefilah link mentioned above, the compiler provides two extended quotes from collections of Merkavah literature (P'sikta Rabati and Otzer Ha-Midrashim, the Einshtein edition). These quotes give detailed accounts of the divisions of angels singing praises in turn. There, it uses the language of r'shut, permission. As one division of angels finishes their praises, they "give r'shut" to the next division of angels to begin.
As to the question of free will among angels which the original question raised, I still think their "permission giving" is more of a formalized "making space" for the next division to begin at a preordained time rather than a free will decision to now allow others to have a chance to sing. If you read the Merkavah quotes, it sounds much more like a ritualized military change of guards than an open mic night where performers can decide and control when they will step aside for another performer.
Tosfos to Chagiga 13b explains as follows (translation my own):
מזיעתן של חיות. ויוצאים ממנו מלאכים ואומרים שירה ומיד נטרדים והכי מצינו במדרש (איכה ג) חדשים לבקרים שבורא מלאכים בכל יום ואומרים שירה ונטרדין להן כדאמר בסמוך משום שיש אות במלאכים הקבועים שממתינים זה לזה לומר שירה ואלו החדשים שאינם יודעים הדת ממהרין לשורר ונתחייבו כליה והיינו אשר תקנו ויסדו אנשי כנסת הגדולה ביוצר ונותנין רשות זה לזה קדושה כולם כאחד עונין ואומרים
Angels come out of [the sweat of the Chayos] that sing praise to Hashem and immediately cease to exist. We thus find in the Midrash "They are new every morning" - Hashem creates new angles each day, and they sing praise to Him and then cease to exist. This is because there is a sign by the permanent angels who wait for each other to sing praise, and these new ones are unaware of this protocol and sing before their turn and are liable to be destroyed. This is the meaning of the prayer established by the Anshei Knesses Hagedola "And with love grant permission to each other etc."
Tosfos quotes a Midrash which explains that there are two different types of angels. Some angels are permanent, while others exist for a split second and then cease to exist. Their essence then drops into the river Dinar, which flows into Gehinom and stokes the fires over the heads of the evil "residents" there. The permanent angels wait to offer praise to HaShem until they are given permission to do so; whereas the temporal ones achieve reality and immediately give praise to HaShem without waiting for permission, and this causes their early demise into the river Dinar.
The commentaries on Kedusha of shemoneh esrei (Avudarham among others) say that the angels are requesting permission from each other in order to start together. It therefore seems that they do not need the permission because they can't praise Hashem were it not for another angel allowing them to, rather the permission is a way of expressing that they make sure everyone is ready to begin at the same time.