I sggest you tke the train to Prien .From in front of the Prien station take the bus to Reit im Winkl. Tkes a bout 45 min. There pick up an Austrian bus to Koessen. .For the Munich - Reit im Winkl section, go to www.bahn.de for schedules, incl. the bus.
Specifically, from the airport take the S-Bahn suburban train to the Munich Ostbahnhof (East station), that's where all the trains heading east (i.e. Prien, Salzburg, etc.) leave. For the section Munich Airport - Reit you can use the Bavarian Ticket, EU22 for one person.
To use this ticket, you must limit yoursaelf to local trains. Regio trains and the bus. These local trains take about 20 minuteslongedr to Priuen than the fast IC and EC trains, which are much more expensive. You can get all the details on the Bavarian ticket in "search" in the Germany Forum.
When I lived near Reit, there used to go a bus from Prien direct to Koessen, via Marquarstein, but I am fairly sure it no longer runs. But just to be sure, also check Munich - airport to Koessen.
EXACT dates and EXACT times of arrival and departure.
The bus from Prien to Reit im WInkl takes ~ 50min - 1hr
Although the distance is short from Reit im WInkl to Kössen the Postbus 4000 line from Reit im WInkl to Kössen does not run very often
Other easier way may be over Kufstein.
From there you can pick up direct Intercity EC trains to Kufstein or combination of 2 Regional services over ROsenheim to Kufstein
From Kufstein then take the 4030 Bus to Kössen.
The bus takes 45-50mins from Kufstein to Kössen. Costs €6
You can use Austrian rail www.oebb.at to show the overall solution from Munich Airport (Flughafen München) to Kössen
A ticket from Munich Airport to Kufstein utilising the direct intercity bought on the day would cost €28.50
If you use the Regional services to Kufstein then a standard single is €22 (same as the Bayern Ticket).
There isn't much difference in time between the Intercity and Regional connections. From the Airport it takes 1h50 to Kufstein (with 1 S-Bahn and 1 Intercity) or 2hrs (1 S-Bahn and 2 Regionals)
the Bayern Ticket. Costs €22 for 1 person then €4 for each additional person up to a total of 5 people. Gives you UNLIMITED use of ALL Regional public transport in Bavaria. Includes ALL Regional trains, ALL Regional buses and ALL city transport in Munich, Augsburg and Nürnberg.
Only the fast ICE, IC, EC and RJ Railjet trains are excluded
Valid from 9am weekdays (midnight weekends) until 3am the following morning
Full T&Cs and click on Bayern
AUSTRIAN TRAVEL INFO
You can use www.oebb.at to show train/bus connections/solutions from Munich Airport to Kössen
www.vvt.at for public transport in Tirol
Thank you so much, this has been very helpful. I arrive in Munich airport at 11.30am Wednesday the 27th of February. I plan to return from Kossen on Sunday the 3rd of March at approximately 16.00hrs...