If you want to render larger versions of Flare art, in Blender just change the render size (keeping the same aspect ratio). In the Properties window, the Render tab has a widget named "Dimensions". You should see the X,Y resolution there.

A few warnings:

Some of the art is not set up for easy one-click rendering. Some of the character and spell art has a python script to rotate and render the scene, so Run Script is used to render all the frames. Some tile set pieces have animations instead, so the Animate button is used to render all the frames. But sometimes it takes manipulaing the scene between each render (often rotating and moving objects; in rare cases, changing textures or scene options).

Storing very large images like that will take up more memory than you think. Currently Flare takes up about 100MB at runtime for images; if you scale up to 512x256 (8x) it would require 64x more memory (remember, that's 8x in both dimensions), over 6GB of video RAM. I'm not sure if video cards even go that high yet? Some video cards may not even hold images above a certain size. Map loading will be quite slow. etc.

Finally, most of Flare's older art isn't designed to look good at larger sizes. It's going to be ugly at 512x256.

It only uses the images it needs, correct. But on a given map it needs the hero, any creature on the map, and the map's tile set.

Reminder, it's held in memory uncompressed (32 bits per pixel). The file sizes you see for the .png files are highly compressed. Try converting the png files to BMP to get an idea of how much space they take up in memory.

You've missed a point -- the size of the png files is irrelevant. Once it's in memory it has to be completely uncompressed to be useful. It's going to be 32 bits per pixel in memory no matter what you do with the png files.