If hiking the King's Trail, you will most likely be starting your hike at Abisko in the very north of Sweden. So you would most probably get there from Kiruna (by train, bus or car), and you would in turn be flying to Kiruna from Stockholm. So your main options are probably to leave the luggage in Kiruna, or in Stockholm.
In Stockholm, assuming the main Arlanda airport, there's a luggage storage service in Terminal 5, where you would be paying 60 SEK (about 6.5 EUR) to store a typical piece of luggage for 24 hours. Consult this page for details:
The Kiruna airport does not have luggage storage. The main Kiruna central station is currently closed (and will be in August), so a temporary one is being used, and I cannot find whether they have luggage storage. The best option for storing luggage in Kiruna is probably at the city's tourist office, located centrally, where a bag costs 20 SEK per day. The tourist office is however only open during normal business hours, and it may be less convenient for you to take the luggage to Kiruna and back since you don't need it for the hike anyway.
Storing the bags at Stockholm-Arlanda airport is probably your best bet, in the absence of further details.