I hope somebody in that district thought to make rules for three-way ties... otherwise you got a mess coming. The best time to plan for this possibility is when you ORGANIZE your district so that all can make these decisions in a situation where noone can claim that a decision was made to help or hurt any specific team in a specific situation.
In a three-team tie (or any more-than-two-team tie, since a two team tie can usually be easily broken by their head-to-head meeting), the first thing you should do is determine the records in the games involving the teams that are tied. If it's a three-way tie, but Team A is 2-0 (wins over B & C), Team B is 1-1 (win over C, loss to A), and Team C is 0-2 (losses to A & B), that breaks the tie. But usually, all three are 1-1 (A beats B, B beats C, C beats A) which means you need to go another route.
Point differential is most common (usually with a point cap, 14 to 21 points max per game to discourage the idea of running up the score so to take away the excuse that you had to run up the score to insure point differential).
If a tie remains between two teams, you can then go back to head-to-head meetings. If it's still tied, other metrics like total points allowed (either among the teams tied or in district play) can be used, but it's rare to have to go beyond the differential (in fact, the differentals above: +3, +2, -5, are among the closest I've seen).
Coin flip should be the LAST option. Heck I'd almost say pistols at ten paces should come before a coin flip. Almost.