Probably not worth the effort unless they seem too crowded or are drying out too fast.

Ditto as gigor.
If they are too crowded in flat and they are too small, I would pot them, to give the some time ti get bigger before planting in the bed.

I think I'll try potting some of these up.......... (maybe 2 of the 6 flats) At what stage/size should they be potted up?

Always have wondered how commercial growers produce such stocky transplants.......

I was at my wholesaler today picking up seed potatoes & one of the warehouse workers said they had just gotten in a semi load of onion transplants..... I was trying to do the math on how old those transplants would be from shipping until they were planted in people's gardens here in NE Kansas.... I'm guessing at least 8 weeks! Another good reason to grow your own!

At what stage/size should they be potted up?
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It all depends on your comfort level and how you can handle small seedlings with YOUR handS. BUT I assure you, that you cannot kill an onions seedling very easily.

I would water them real good, then separate them, lay them on the ground ( on my right hand side). Now my pot is on my left land side, filled and ready. Withe a pencil( or my finger) I make a hole ; Take a seedling (holding it from middle); Drop the root/bulb in the hole ; REPEAT.
At the end lightly pack and level, WATER. If they get crooked, straighten them up.
THAT IS ALL THERE IS TO IT.

IMHO,
Commercial growers like Dixondale, that sell big, stocky, bare-root transplants are direct seeding in the ground, not growing in flats. They are also pumped on fertilizer.

Most of the onion seedlings that get sold in 6 packs or those little 4x6 plastic pots are tiny and crowded.

I agree that you're better growing your own.

-Mark