There is no set universal scale, every plate is to scale but with different scales. Essentially, they scale the place to show the representation required to orient the pilot. When these plates are printed out they may be resized by software, so even saying X mm is 1.25NM won't work.
It sounds like you might want to superimpose a plane on the plan view, which is going to be challenging in many ways. Detecting scale is possible by measuring distance between CUTIS and CFVGK as others suggest, however that will be difficult to do programmatically because these are meant to be interpreted by squishy carbon units. Look at CUTIS:
CUTIS is the place where the squiggly line meets the thin line cutting across the arrow.
Programmatically determining exactly where to start your scale measurement will be extremely difficult, if you have it wrong by a few pixels that will translate into the wrong scale and your airplane symbol in the wrong place. If you solve that problem for this plate there's hundreds more that look different. There's so many edge cases you'd have to code around, it's unlikely you'd ever get them all.