Barnen syns bättre med reflex på sina jackor.

Barnen is the definite plural form: the children.

The noun goes like this:

• ett barn = a child
• barn = children
• barnet = the child
• barnen = the children

So the sentence is talking about a specific or understood group of children, not just children in the most indefinite sense.

Syns is the present tense of synas.

In this sentence, synas means:

• to be seen
• to be visible
• to show up

So Barnen syns bättre means something like:

• The children are seen more easily
• The children are more visible

This is a very natural Swedish way to say it.

Because the children are not the ones doing the seeing.

• ser = see
• syns = are seen / are visible

Compare:

• Barnen ser bilen. = The children see the car.
• Barnen syns bättre. = The children are seen more clearly / are more visible.

So the focus here is on how visible the children are to other people.

Bättre is the comparative form of bra and means better.

Here it works adverbially, because it describes how the children are seen:

• syns bättre = are seen better / more easily / more clearly

It is irregular, just like English good → better:

• bra = good / well
• bättre = better
• bäst = best

So you do not say brare.

Because reflex is being used in a general way here.

In Swedish, reflex often means reflective material or a reflector used for visibility in traffic. In that kind of context, Swedish often uses the noun without an article:

• med reflex = with reflective gear / with reflectors / with reflective material
• med en reflex = with one specific reflector

So the sentence is not stressing the number. It is stressing the idea that the jackets have something reflective on them.

Yes, absolutely.

• med reflex sounds more general
• med reflexer sounds more countable and may suggest several separate reflectors

Both can be natural, depending on what you want to emphasize.

So:

• Barnen syns bättre med reflex = focus on reflective visibility in general
• Barnen syns bättre med reflexer = focus on actual reflectors as separate items

Because sina is the reflexive possessive form. Swedish uses sin / sitt / sina when the possessor is the subject of the clause.

Here, the subject is Barnen, and the jackets belong to the children themselves. So Swedish uses sina:

• Barnen syns bättre med reflex på sina jackor.

If you used deras, it would usually sound like the jackets belong to someone else, or at least it would not point back as clearly to the subject.

Also, sina agrees with jackor, which is plural:

• sin
  • common gender singular
• sitt
  • neuter singular
• sina
  • plural

Because after a possessive word, Swedish normally uses the noun without the definite ending.

So you say:

• min jacka = my jacket
• hans jackor = his jackets
• sina jackor = their own jackets

You do not say:

• mina jackorna
• sina jackorna

So sina jackor is the correct form.

Because på means on, and the reflective material is located on the jackets.

The structure is:

• med reflex = with reflective material / with a reflector
• på sina jackor = on their jackets

So the sentence literally says that the children are more visible with reflective material on their jackets.

No, this is standard Swedish main-clause word order:

• Barnen = subject
• syns = verb
• bättre = adverb/comparative
• med reflex på sina jackor = prepositional phrase

So the pattern is basically:

Subject + verb + adverb + extra information

You can also move the last part to the front, but then Swedish keeps the verb in second position:

• Med reflex på sina jackor syns barnen bättre.

That is also correct.