Does Gust counter Shuriken Flip if they aim at something I have?

No — Gust doesn't counter Shuriken Flip; the spell still resolves, Gust just blanks whichever instruction was aimed at the unit it bounces.

If they Gust your friendly unit (3 Might or less, at a battlefield — a unit at your Base isn't a legal Gust target), that unit goes to hand, so the "move a friendly unit" instruction mistargets and does nothing (Rule 359.3.e.7). But Shuriken Flip's two instructions aren't linked — no "if you do" — so the "Deal 2 to up to one enemy unit at a battlefield" half still resolves and still deals its damage. Conversely, if they Gust the enemy unit you targeted for damage, the damage whiffs and your move still happens (same logic as the Flash ruling, FAQ #12618).

The only real "counter" here would be an effect that actually Counters the spell, which puts it in the trash and means it was never played (Rule 426).