Which method can be used to determine the pKa of an acid-base indicator like bromothymol blue?
Yes, HCl would work with a pH meter. If you know the mass of base (indicator) you use, you can as 0.5 equivalents of a strong acid such as HCl and determine the pH. At that point, since the weak base would be half protonated, the pH would be equal to the pKa, based on the Henderson-Hasselbalch equation. Or you could just so the whole titration and find the pKa halfway to the equivalence point.

In this case, you have to make sure you start with the basic form of the indicator, however. Not sure what form it is supplied in.