Control Flames will work on normal fires started by magic.
None of these spells produces a magical fire. They use magic to start a fire.
You instantly light or snuff out a candle, a torch, or a
You instantaneously light or snuff out a candle, a
torch, or a small campfire.
A flammable object hit by this spell ignites if it isn't being
worn or carried.
You'll notice that all of the things that might be lit by these cantrips have normal fuel (oil, wood, etc.). They are not fueled by magic (unlike Create Bonfire). Magic was only used to create the initial spark. The cantrips above take place instantaneously and are not sustained by the magic or caster.
Other Magic which starts normal fires through instantaneous ignition:
- Flaming Sphere (2nd level) - for the things it ignites
- Fireball (3rd level)
- Lightning Bolt (3rd level)
- Delayed Blast Fireball (7th level) - despite the concentration, the explosion is instantaneous
- Fire Storm (7th level)
Magic which sustains a magical fire for an amount of time:
- Create Bonfire (cantrip)
- Continual Flame (2nd level)
- Flaming Sphere (2nd level) - the sphere itself
- Heat Metal (2nd level) - within the metal itself
- Flame Blade (2nd level)
- Fire Shield (4th level)
- Wall of Fire (4th level)
- Incendiary Cloud (8th level)
There are also other fire spells which do not start fires, such as Chromatic Orb (fire) and Flame Strike. (All of these spells are in the PHB except Control Flames and Create Bonfire from XGtE.)
You can expand the fire into an adjacent 5' cube (containing fuel) each time you cast this cantrip.
If you spend 1 action to expand the fire into each ground level cube of the barn, the fire will do the rest. This might even be overkill, but you might as well keep expanding it since you're already standing there watching it (from within 60').
(Control Flames lets you sustain 3 non-instantaneous effects on the fire at once. You don't need any of those.)
Also note that you could just use the Firebolt cantrip (120') itself to start the barn on fire without getting so close.
Control Flames (60') could also be used, but would not be necessary. This would be safer than having to walk up to the barn with a torch in order to cause it to spread.