Well as you seem to be witnessing with your own eyes Chickens can very clearly vomit. They can do this after drinking excessive amounts of water particularly in very hot weather it helps cool them. It can also be indicitive of sour crop or impacted crop. The 'vomit' is usually clear water. Dark coloured chx such as Barnevelders, or RIR or Black Rocks,are more susceptible to heat stress than light ones such as Light Sussex. Make sure they have access to clean cool water kept in the shade all the while and they have shade in their run not just in the house.
Check their crops, which is the food sack at the bottom of their necks to the right, and particularly note any foul or sour smell. At the end of the day their crops should feel full and reasonably firm though not hard. If their crops are still full in the morning before you let them out it may indicate either sour crop or impacted crop. Sour crop is a result of feed in the crop starting to ferment and the crop usually feels full and mushy hence the smell whereas impacted crop feels hard and is due to a blockage. Both conditions need to be cleared and your intervention may be needed if either is indicated. Sour crop can be cleared by inducing 'vomiting'. Though don't do this for impacted crop refer to specific information on these conditions if they are indicated.
If this is sour crop make sure it's not been caused by eating grass cuttings which very quickly ferment once cut. People do give chx grass cuttings but it's not a good practise because of the dangers of sour crop or impacted crop caused by eating very long pieces of grass. Fresh grass firmly anchored is best so they can nip off small bits.
I don't think what you are seeing is anything to do with respiratory disease which would be indicated by cold type symptoms such as, nasal discharge, runny eyes, swollen sinuses, wheezing, rattly breathing or breathing difficulty such as gaping. They may well also be depressed with tails down and disinterested in food or moving about much and generally look miserable. If your hens show these symptoms (usually more than one) suspect a respiratory disease which will need a vet visit to get antibiotics.
Having checked out for potential crop problems I'd keep your chx under observation for any symptoms of depression or other illness but if they are otherwise OK and engaging in normal chicken behaviour like eating drinking ,foraging and scatting about, grooming and being active I'd not worry.
If these are farmyard birds I'd worm them as soon as possible using Flubenvet. It's just possible worms could be causing the apparent vomiting too.