Your approach is indeed unconventional! Let’s break it down:
Technical Skill Display: By using Flexbox and Docker, you’re showcasing your knowledge and proficiency with modern Web Design and container technologies. This can be quite impressive, especially for positions that value innovative problem-solving and technical skills. In this regard, your approach scores high – around an 8 or 9 out of 10, as it demonstrates creativity and a practical application of technical knowledge.
Relevance to Job Applications: Whether this method will help you land a job depends on the role you’re seeking. For tech positions, particularly those involving front-end development or DevOps, your novel approach could grab attention. However, for non-technical roles, traditional resumes might be more appropriate.
Presentation and Accessibility: One consideration is how accessible this format is for recruiters. Many employers use Applicant Tracking Systems (ATS) to scan resumes, and a Docker container won’t interface with these systems. To ensure your resume gets into the right hands, consider including a link to your traditional resume as well.
Uniqueness: Your distinct approach might make you stand out. It shows initiative and a willingness to experiment – qualities many employers appreciate. However, ensure it doesn’t come across as a gimmick if the rest of your application materials and professional story don’t support this tech-centric narrative.

In conclusion, while your strategy is innovative, make sure to complement it with a conventional resume to cater to a wider range of application processes. It could certainly catch the eye of tech-savvy recruiters, but balance and clear communication of your skills and experiences remain key.