Autonomous web agents increasingly operate over sensitive personal data, yet existing privacy-preserving approaches rely on static filtering and globally enforced safeguards misaligned with compositional agent execution. We introduce PrivAgentFlow, a memory-guided agentic workflow framework that formulates privacy preservation as adaptive node-level governance over compositional web-agent workflows. PrivAgentFlow decomposes complex tasks into compositional workflow nodes, where each node operates under a distinct privacy policy conditioned on its execution role and information access requirements, enabling privacy governance to be localized at the execution level rather than globally enforced. Such localized governance is refined through execution memory, where historical task failures and privacy violations serve as corrective signals for improving node-level privacy control without exposing raw user data during planning. We provide theoretical insights showing that compositional web-agent workflows induce subtask-specific privacy–utility trade-offs, formally characterizing the advantage of heterogeneous node-level governance over uniform privacy control. Across 246 web-agent tasks on three platforms, PrivAgentFlow improves task utility by 23.1 percentage points (0.415→0.646), cuts environment-level privacy leakage by 92.3% (0.366→0.028), and reduces API-level leakage from 100% to 3.7% over the strongest prior baseline. Our code is available at https://github.com/haorentang/PrivAgentFlow.