Evolutionary multi-task optimization (EMTO) is an advanced optimization paradigm that improves search efficiency by enabling knowledge transfer across multiple tasks solved in parallel. Accordingly, a broad range of knowledge transfer methods (KTMs) have been developed as integral components of EMTO algorithms, most of which are tailored to specific problem settings. However, the design of effective KTMs typically relies on substantial domain expertise and careful manual customization, as different EMTO scenarios require distinct transfer strategies to achieve performance gains. Meanwhile, recent advances in large language models (LLMs) have demonstrated strong capabilities in autonomous programming and algorithm synthesis, opening up new possibilities for automating the design of optimization solvers. Motivated by this, in this paper, we propose a Self-guided Knowledge Transfer Design (SKTD) framework that leverages LLMs to autonomously generate knowledge transfer methods (KTMs) as algorithmic components within EMTO. By enabling data-driven and self-adaptive construction of transfer strategies, SKTD facilitates effective knowledge reuse across heterogeneous tasks and diverse EMTO scenarios. To the best of our knowledge, this work represents the first attempt to automate the generation of KTMs for EMTO. Extensive experiments on well-established EMTO benchmarks with varying degrees of task similarity demonstrate that the proposed SKTD consistently achieves superior or highly competitive performance compared with both the state-of-the-art program search approach and manually designed EMTO methods, in terms of optimization effectiveness and cross-scenario generalization.