Multimodal Large Language Models (MLLMs) achieve strong performance through instruction tuning, yet real-world deployment often requires continual capability expansion across sequential tasks. In such scenarios, Multimodal Continual Instruction Tuning (MCIT) aims to acquire new capabilities while limiting catastrophic forgetting. Existing methods mainly follow a module-composition paradigm: they maintain task-level prompts or LoRA experts and dynamically route or aggregate a subset of them at inference. However, samples within the same task can still differ substantially in visual scenes, question intents, and reasoning demands. This motivates instance-level adaptation to individual query-image pairs rather than only selecting or combining task-level modules. To this end, we propose DRAPE (Dynamic Cross-Modal Prompt Generation), a prompt-learning framework that synthesizes continuous instance-specific soft prompts for MCIT. Instead of selecting prompts from a fixed pool, DRAPE derives prompt queries from the textual instruction and cross-attends to visual patch features, producing query-image conditioned prompts that are prepended to the frozen LLM. To mitigate forgetting during sequential updates, DRAPE applies null-space gradient projection to the shared projector and uses CLIP-based prototype routing for task-label-free generator selection at inference. Extensive experiments on MCIT benchmarks show that DRAPE achieves state-of-the-art performance among representative prompt-based and LoRA-based continual-learning baselines.