Unfortunately, there isn’t any direct flights between Yakutsk and Magadan. The Republic of Sakha and Magadan Oblast do not keep intensive business/trade/tourism relations. Consequently, no strong demand for regular flights.
However, people have TWO ways to reach from here to Magadan:
1. By plane. Through the third city, for instance, Khabarovsk.
2. By car. Btw, no car rent is available in Yakutsk. But you may find drivers going on your way. Many private ads appears in newspapers or on TV, saying “Give a ride [to certain place].” Usually, people goes by ground or air to Ust-Nera, where they can easily find a sort of long distance taxi (minivan for 7-8 passengers) going to Magadan.
There are flat rates for a ride. Here are long distance taxi rates: 3000-4000 rubles for a ride from Yakutsk to Ust-Nera as well as from Ust-Nera to Magadan.
If you want to be the only passenger, driver will charge you about 2000 EUR for your trip on the route Yakutsk – Magadan in winter time. This is not a joke, unfortunately. The Kolyma road is not safe. Apart from car lost risk, high price is set, because a driver need to come back to Yakutsk. In summer the rate is less a little bit.
But! Remember, in our region everything depends on your ability to negotiate, and in any event rates remain high enough, because private drivers are not Greyhound employees.
The Kolyma Highway / the Road of Bones travel map

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UPDATE, May 28, 2009:
Yakutia Airlines launched flights on the route Yakutsk – Magadan – Petropavlosk Kamchatsk for 2009 Summer. More info in the post “2009 Summer Flights Schedule – to/from Yakutsk”