I was booked on a work trip that goes from the US thru Frankfurt and on to the Middle East. I had to change my plans and the cost of rebooking the ticket would have been very high, so the travel agent said to book another ticket. So, I did. I now have a second ticket from Frankfurt to Amsterdam and a couple days later I continue on from Amsterdam to the Middle East. The first booking is thru Lufthansa and the second is with KLM. Has anyone had experience getting the ticket agent to book your luggage thru to your new final destination if you show them both tickets? Is my only option to not check luggage?
First, are you aware that if you miss any legs in your first ticket, the remainder of the ticket is likely to be cancelled? If you have a oneway journey, this is not a problem. If you are hoping to pick up the first ticket again later to go home, after missing your Frankfurt to Middle East flight, your first ticket will now be void and you will need to buy a new ticket to get home.
Checking luggage across separate tickets is sometimes possible but it is fraught with uncertainty. It is very hard to give a guarantee that it will be possible. In recent years, a number of airlines that did offer this service have withdrawn it (for instance, American Airlines, British Airways) and will now refuse to do it.
When it is permitted by airline policy, it is a slightly complicated procedure that may require a more experienced agent to do. Sometimes, less experienced agents will deny that it is possible or allowed even if the airline permits it.
Also, it is usually only allowed between the airline's closest partners, those in the same airline alliance. In this case, KLM and Lufthansa are competitors in two different alliances. I think it unlikely that your bag will be checked through. Even if it is checked through in one direction, that is no guarantee it will be checked through in the return direction.
(On top of this we require the airlines to have a baggage interline agreement with each other for legal reasons, this almost always satisfied between major airlines.)
I would also caution you that trying to re-route bags manually like this makes it much more likely that your bag will go missing for a few days. Be sure to show your baggage receipt to your onward airline so that they know to expect an extra bag for loading. In my case I have permanently lost three bags this way.
I would advise against checking a bag on your itinerary, unless you have enough time to collect it and check it in again between your tickets. It doesn't hurt to ask if it is possible, but I would not rely on that.