Using my imagination and assumptions because of information not provided –
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Dream School – If you are talking about a college with highly selective admissions and his application had the support of the coaches this year, but he was still not admitted – Then, it sounds like athletics was not the problem and is unlikely to be the solution. Time to move on.
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What can coaches do – You have to ask each coach, but your posts suggest admissions was the issue not the roster spot.
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Transfer to a top school – Since you describe him as a D2/D3 level athlete, I assume you are talking about a top academic school. Again, it goes back to admissions. Perhaps look at a couple years of Common Data Set information to gauge how many students transfer each year into the colleges of interest. But, I would think long and hard about how focusing on transfer before even starting College could be setting your son up for a 2nd year of stress, anxiety, and potential disappointment.
Unsolicited advice: (1) go back to the coaches your son turned down and see if they can still help him get in; (2) tell the dream school coach your son put all his eggs in one basket and ask if he has any connections at similar colleges that might consider a late application where he might be a good fit; (3) find colleges with swim teams that are still accepting applications (search “best colleges still accepting applications”). Last year, many good colleges had trouble filling their classes and that trend might continue this year.