I personally would not use that, it's for pain or fever. I did find a study that was done in Egypt that used medications for heat stress, link here:
https://www.cabidigitallibrary.org/doi/full/10.5555/20053017027
They did not have data from long term use.
All those frozen vegetables may be causing some digestive upset, anything other than feed should be limited to no more than 10% of their daily diet. If they seem hot, change their water more often to keep it cool, add frozen water bottles to waterers to keep it cool, give them open shallow pans in the shade filled with water that they can stand in, I often leave a hose on trickle in the shade, where they can stand in it which is always popular. Make sure they have shady areas, if you have a safe place to put a fan (an inexpensive box fan works well), to move the air it can help. I also sometimes hang a frozen jug of water in front of the blowing fan, does cool better, primitive air conditioning. I have cooled my coop on occasion that way. Some use misters to help lower the temp a little. Actual temperature and comfort can be affected by humidity and dew point, so may feel hotter than what the thermometer says, I'm not there, so can't say. Without having a better idea of your set up, breeds, ages, other variables, it's hard for me to know. I deal with high humidity all the time here in Florida, we've been having heat indexes north of 100 F for weeks here, so it's a constant issue for me, this summer has been particularly hot.