You can try by MS monitoring the intensity of the analyte peaks. The basic kinetic model is given in:
Quantitative collision induced mass spectrometry of substituted piperazines – A correlative analysis between theory and experiment, Journal of Molecular Structure, Volume 1149, 5 December 2017, Pages 243-256, B. Ivanova, M. Spiteller
You can use only ESI or APCI via a single operation mode; or coupled with CID.
In particular, pay attention to the reference section of the manuscript shown above.
There are ELISA test kits for high sensitivity AMP detection. I've used this for G-protein coupled receptor/adenylate cyclase kinetics. You take timed samples from your assay solution and add them to the ELISA wells recording the start times for each ELISA well. Then you quench each well as the color develops to get the end times. The AMP concentration is interpreted from the ELISA reaction RATE (delta AU/time), not the final concentration. It's tedious, but works really well.
Your question implies that pyrophosphate is also a product of the reaction. By coupling your reaction with pyrophosphatase you can generate two molecules of Pi per molecule of ATP hydrolysed. Measurement of Pi is routine.
First off the other answers here are all great and should work well (MS, antibodies, etc). These are methods that generally require quenching the reaction then detecting after that, which can be a bit laborious if you want enough data points for good Michaelis-Menten kinetics. A continuous, non-quenching method you could try to adapt is based on detection of the proton released during ATP hydrolysis.
At pH above the pKa of phosphate the reaction is as follows (according to paper in first link below):
ATP(4-) + H2O -> ADP(3-) + HPO4(-) + H(+)
If your reaction forms AMP and diphosphate this might still hold. The key is that a proton is formed, and if the reaction occurs at a pH around 8 that proton won't go to the phosphate or diphosphate. You might therefore be able to use the method in the linked Janes et al paper to monitor release of this proton colormetrically, in real time, using a pH indicator. This paper uses 4-nitrophenol at pH 7.2 but you might need to adapt it to a pH indicator and reaction pH that is higher to ensure the pH indicator gets the proton instead of phosphate (eg phenol red as indicator and EPPS as buffer at pH 8).
Again, the other methods might work better, but if you want to try a real-time assay this might work as well.