If you can only capture 60FPS, you cannot accurate measure a signal of 40Hz, since it is below the Nyquist frequency. (I know you mentioned the slow-mo camera which probably does have the bandwidth).
Frequencies beyond the Nyquist limit alias back to resolved modes. So a combination of the camera plus a human eye to check that the flashing is “fast” (i.e. above the Nyquist limit) should be enough to verify the frequency.
You technically can measure over the nyquist frequency, for example here if you measure 80Hz with your 60Hz camera, you can be sure that either you really did the math wrong with the intended 40Hz, or it is actually the nyquist shadow frequency of your 40Hz oscillation!
Of course, you’re right about the Nyquist frequency (how could I forget the Nyquist-Shannon Sampling Theorem!). But I looked it up and the iPhone 15 slow motion mode can do up to 240 fps which is enough to easily measure it super accurately with a short sample.