SN754410 output supply current - heating
According to the data sheet, at 1A, the typical voltage drop per half bridge will be 2.6V. Assuming you have two half bridges energized 100% of the time, the total power dissipation at 0.6A (assuming the same voltage drop, which is a bit pessimistic, but they are 'typical' values, not guarantees) is 3.1W. 



That doesn't even include the 20 to 70mA of supply current, it's just the output drop times the current. At 24V/5V, the additional power dissipation due to the supply current (half high, half low) is 0.27W max (from 5V) and 0.64W max (from 24V) for a total of 4W.  

That's clearly in excess of the absolute maximum power dissipation rating of 2W at 25°C free-air \$T_A\$, so you're way over what that chip is capable of safely handling. If you want it to work with \$T_A\$ = 50°C you need to keep power dissipation under 1.7W, as per "Note 2".  




Always carefully read the fine print in datasheets. When they say "1A capability per driver" that often means that you can only use one driver at once, and maybe not continuously, and often not at the maximum temperature.