Has the branch asked members to burn old books? No
Has the branch asked congregations to burn older items?
Each year, individual branches send letters to the congregation instructing which items to display, and which to discard. Our congregation, being a non-english congregation, asked the branch to elaborate what 'discard' means. The branch replied that discard meant to remove them from the Kingdom hall, by either giving them out to the publishers who needed them, and if no one needs them, then destroy them rather than letting them rot in the storeroom.
What about older publications from the Library?
Below are the latest instructions (as of 2020):
"Since some publishers and interested persons do not use computers or electronic devices, the elders should give careful consideration to the needs of such individuals when making decisions as to the Kingdom Hall library, especially before deciding to eliminate printed publications. If the publications will be provided in electronic form, such as on a device or on a computer, a printer should be made available. At least one responsible brother should be assigned to keep the library up-to-date and in good order.
In the event that the bodies of elders decide to eliminate printed publications from the library, care should be taken not to discard items that have historical significance. The branch office may wish to add such items to its library or to its archive of historical materials." - sfl Chap 21, Para 39-40
Not sure about other countries, but here there is no direction to destroy all older books. Most of the older congregations still have libraries with one copy of each printed publication.