There is no maximum value that you can write in an AMPL .dat file. However, if you write a value that is larger than what can be represented in the computer, then when you try to display the value, AMPL will show it as "Infinity". AMPL uses the computer's "double precision" representation for data values, which gives a largest representable value of approximately 10 to the power 308.
But you should never use such a large "big M" value in your data. In general, you want to choose M to be large enough to make your results correct, but not too much larger than that. See my discussion of
The Big M for a more detailed explanation.