I believe that the second sentence of RRS 61.1a answers your question.  The flag and hail is required if you are intending to protest.  The third sentence of RRS 61.1(a) tells you how long you have to fly it once you have raised it.  In the case you describe I would look for the flag to be displayed until the boat has finished the first race of the day.

The interesting question is how long do you have to display the flag if the incident happens in the racing area after the last race of the day as the boat is no longer racing for that day?  I suspect it is sufficient to display it until the other boat is informed that they are being protested.

"...However, a boat not racing shall not be penalized for breaking one of these rules, except rule 14 when the incident resulted in injury or serious damage, or rule 24.1" - Preamble of part 2

"if as a result of the incident a member of either crew is in danger, or there is injury or serious damage that is obvious to the boat intending to protest, the requirements of this rule do not apply to her, but she shall attempt to inform the other boat within the time limit of rule 61.3." - 61.1 a) 4. 

So, in my opinion:
- If any boat suffered clear damage or Injury, there is no need for the flag ;
- If due the incident a boat could not start, so could not race, there is no need for the flag ;
- If there is no clear damage or Injury, but this can be a point of discusion during the audience, rule 61.1 a) is clear and the flag needs to be displayed until the boat has finished the first race after the incident.

If there was no Damage/Injury and 24.1 was not in case, so the protest is invalid, with or without the flag.

John stated a good point. 

In my opinion, when the Incident happens after the race, the boat was no longer racing so 61.1a) no more requires the flag.

And what if all the races were abandoned for that day and a protest about an incident before the races is presented anyway? 

There was an appeal that came out of a protest over an incident that occurred at the finish line of a race in a North American championship of a keelboat class a couple of years ago.

The protestor did not fly a flag, arguing that since both boats had met the definition of finish, there was no need for a flag.  The protest committee disagreed and declared the protest invalid.

The Regional Association Appeals Committee upheld the protest committee's decision.

When in doubt, fly the flag and keep it flying.  It never hurts, and can only help your case. 

Tom doesn't tell us what the other boat was doing.  She may already have been racing, perhaps pre-start; she may have been 'in or near the racing area and intending to race'; or she 'have been racing'.  In all those case the RRS would have applied and the boat would have been entitled to protest.  In all those cases the incident would have necessarily have been in the racing area so the injured boat must fly a flag (unless one isn't needed under rule 61).  There may have been another reason of course, such as a breach of class rules or the like, so that the breach was not in the racing area, when a flag would not be needed.

If I was sailing the injured boat, I would have flown a flag anyway, just in case!

I think this is the best answer here. Regardless of whether a boat is racing or not, 61.1 and the preamble to Part 2 apply; the boat is in the racing area and intending to race, as such the hail and flag requirements apply to her. I should have clarified that the other boat was also intending to race (so we wouldn't go down the IRPCAS rat hole), such that Part 2 would apply to both boats.

I had a similar protest a couple of years ago, and if I recall I allowed the protest (there was a notify the RC provision in the SI's as well that the competitor did comply with). I've since thought that decision was incorrect, and this appeal decision confirms my mistake. I'd agree that the flag simply needs to be up long enough so that the protestee is informed. If it's me, I'd leave it up until we get to the dock to be sure.

Agreed, and if the SI's specify a notify the RC requirement, I'd expect the protestor to notify the RC following that race.

Assuming the protest was valid (e.g. hail, flag, etc.), but the incident didn't meet the preamble requirements for penalty (e.g. injury, serious damage or 24.1), then a boat could still break a rule, but would not be penalized for it, meaning the protest is valid, a boat could have broken a rule, but no boat would be penalized.

That said, if the incident did result in injury or serious damage, per the preamble to Part 2, they can be penalized. To what race do you penalize them? My gut here tells me the next race. But I do find Rogèrio's last point interesting, what if the incident occurs in the racing area prior to a scheduled race, but that race (and any remaining races) are abandoned for the day? Clearly the boats were intending to race, but no race ever happened. Would you go back and penalize the previous race? I think that as the preamble to Part 2 still applies, the closest race would be the race most recently sailed, and thus that's the race you'd penalize.