Burn monster cripples you and prevents the use of abilities and it cuts off your escape, and it stops your ult. You have more range than Tyra though, so it's best to just keep your distance from her.
In the start of a round, go near the objective but stay behind and wait for around 5 seconds, then use Scout to determine which way Skye will flank.
This also directly counters Stealth.
It's tempting to get deft hands when you know you'll have difficulty with flanks, but you should get your reload speed from your loadout instead. This will allow you to get cauterize so you can keep down the enemy frontline and help your tank further