Don't use Flash! Flash needs browser plugins and security patches every two weeks. Go for HTML5, which is a browser-native technology. All modern browsers support it, so unless you need to support IE8, HTML5 is the way to go.
You could use a <canvas> HTML element as your basis and then use JS to fetch click events and mouse movement. That way, drawing becomes easy and all you have to do is transfer the mouse movements. You can add text boxes with <textarea> s. Blitting images and computing highlighting or a marker is very easy with a canvas, since you have access to individual pixels and just can add the highlight color to the pixel color.
The whole thing should be quite ok performance-wise. If you need heavier graphics-effects, I recommend adding WebGL to the game, as it allows you to use shaders which are computed on the GPU. WebGL also allows you to use HTML elements, so adding it should be a rather small task, if you already know about graphics programming ;)