Do people flying within Colombia need to show a negative covid test result?
Not for domestic travel at present. No tests or even vaccinations required as of July. Most recent government regulations as of this writing are here- in Spanish.
International arrivals do require RA or PCR tests within specified time windows, or fully vaccinated status (might depend on the origin, best to check that).
For example, LATAM airline says the following:
Of course regulations could be tightened in the future and individual entities could impose more restrictive rules most likely.