Is it permissible to supplicate using the mentioned formula which involves dedicating a specific supplication to each letter of the alphabet?

This supplication does not contradict Islamic law. However, the Prophetic guidance in supplication is to choose comprehensive supplications without striving for rhymed prose, in order to combine the good of this world and the Hereafter, and to free the heart for devotion to Allah, which leads to acceptance. Therefore, one should learn the Prophetic supplications and understand them deeply.