The easiest way to reach Flensburg is either by train or plane + train. Closest airports are (all distances to Flensburg approx.):

From Germany:

Hamburg (HAM, Fuhlsbuettel)
www.ham.airport.de

* 155 km, by car 2 hrs, by train 3 hrs
You can take the train from Hamburg airport to Hamburg main train station (S-Bahn 1, every 20 min, EUR 2,85) and continue by train from Hamburg to Flensburg [approx. EUR 28, see bahn.de] or in order to cut the costs you can find somebody via mitfahrgelegenheit.de, who are traveling the same direction (service is only in German).

If you take the train from Hamburg Airport, we advise you buy a ticket all the way to Flensburg right at the airport station. It saves time and money. If you are more than one person, a Schleswig-Holstein Ticket is the cheapest one you can get. It costs 28€ for one person,  29 € for two, then 3 € for each additional person up to five.

There is also a direct bus to Flensburg, but it only leaves once a day from Hamburg Airport at 18.15 h. The bus stop is located between terminal 1 and 2. It is a Danish bus, Abildskou, which goed to Aarhus. It stops at the main bus station in Flensburg (i.e., ZOB) and costs 24 €.

Luebeck (LBC, Luebeck-Blankensee)
www.fhl-web.de

* 195 km, by car 2 hrs, by bus + train 3 hrs

From Denmark:

Sonderborg (SGD, Sonderborg)
www.eksb.dk

* 45 km, 1 hour by car/bus (no train)
(take a taxi from Sonderburg airport to the bus station [15 min], from there take the bus to Flensburg [DKK 76/EUR 10])

Prices for train and bus tickets vary according to distance and are just estimated here.
Please visit following internet sites for planning your bus + train connection:

www.bahn.de (train + bus connections) 
www.kielius.de (bus connections to/from Kiel to/from Hamburg Airport)
www.scout-sh.de (getting from A to B in Schleswig-Holstein county)

Please follow this link to see a detailed map and the exact location of ECMI in Flensburg and to plan your travel: maps.google.de