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How would I design an experiment to compare the strength of the flexor muscles of the arm in students from my class? How could I use this experimental design to find out whether exercise improves the strength of the relevant muscles?

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Honestly, there are hundreds of studies available on google scholar (Such as this search for comparing muscle strength) that are freely available. Published studies include the methods and training regimens that they used, and describe how it's done so that people can replicate or advance the study.

Go through those, and see how they did it. If there is one that you like, you can replicate it, or you can design your own using some of them as a model.

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A quick answer but generally exercise studies regarding strength have you test their strength before and after a study using flexor exercises, charting the number of weight in lbs or kgs that each person can do. For more scientific studies, different biomechanical measures are used, for instance to check instead of showing workout studies they will measure isometric muscle contractions of different parts of the body. For you, I'd say choose 2 or 3 exercises that workout the flexors, mark the weight or resistance used before the study, and have the students strengthen them(it might be beneficial to do different exercises than the testing ones but these should be fine). Then after the study use those same exercises as before. This will measure both if the exercise worked and the flexor strength. The exercises before and after should have a relevant rep scheme that should be the same, just as 1 set of 20 to failure, or as many as possible with 15 lbs, but for this, it might be more relevant to use an isometric exercise like holding a heavy dumbbell for as long as possible with a weight that allows them to do so for at least 15 seconds for a wider variability and see how long they can hold the weight before dropping, the main reason being that flexors are a type 1 muscle that mostly are built for endurance, so you need to ask are you measuring the endurance of these muscles, the strength they can do, or the strength of the muscles themselves.. use a placebo group that doesn't exercise during the study. Diet and lifestyle of students need to be taken into account as well, age,gender, etc.. all students should have similar attributes

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