Heat shouldn't cause flagstone to chip or sink precipitously. Flagstone is laid in the desert and Florida all of time and there aren't any chipping problems unless the stone in next to a swimming pool. The chemicals in the pool will cause problems.
Cracking and sinking comes from the settlement of the ground. When that happens, there's nothing you can really do without replacing and relaying stones.
It's not that difficult to cut out stone and relay them. You'll have to rent a diamond blade saw for about $75 a day and any stone that you need.
You should also look on Craigslist for a local mason or somebody who has laid flagstone before. With unemployment high, maybe you can get it done for costs better than you would normally expect?
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