The blue flags indicate that you will get an alliance from the marriage. If you hover your mouse over the flag, it will tell you with whom you will get an alliance.
If you are the mercenary company's de jure liege and the holding they have (assuming there is just one) is de jure part of your realm, then with a good opinion of you, you should be able to offer them vassalization and have them accept (assuming you are at least a King). You can't grant land to mercenary companies, so it's usually harder to vassalize them unlike with holy orders. Sometimes they gain land through invasions when someone runs out of money with them hired and they take land as payment. This was the case before the 1.07 patch and I'm assuming it's still accurate.
Helps with arranging marriages, as the other party will gain prestige for marrying into the house of ____ so might be a bit more agreeable to your scheming empire building marriage policy. Also I believe all children in a dynasty are born with a percentage of their dynasty's prestige as their personal prestige, which helps your new rulers with vassal opinion until they gain prestige on their own.
