I have noticed that the 'display_string' function, defined in 'system.inc' does not use the CLD instruction. The said instruction does not seem to be used in 'fasm.asm' either.
Is that because fasm clears the direction flag implicitly in some way, or is there some other explanation?
Thanks.

fasm relies on the convention that DF flag remains cleared by default. So every time fasm changes the direction flag to 1 for some reason (with STD), it clears it back with CLD immediately after.

In DOS interface (SOURCE/DOS/FASM.ASM) you may notice that there is a single CLD during the startup and then DF remains 0 for the entire life of program. In modern systems the DF is already by convention cleared as default, so Windows/Linux versions do not even have that initial CLD. You may find this mention in the Anger Fog's document on calling conventions:

Thanks very much, Tomasz, for a prompt reply. I use fasm on Linux. The explanation you have given makes perfect sense.