You can change the frequent flyer number for earning prior to each flight. Make sure you get a new printed boarding pass so that you can send it in if there is a problem crediting the flight.
Alternatively, if you don't have status in any of the airline programmes and are not using your frequent flyer number to gain benefits such as lounge access, you can ...
Miles are not a currency that can be moved between programmes. There are some exceptions (such as Avios, which can be moved between the British Airways Executive Club and the Iberia Plus) but this is unusual. I am not aware of any SkyTeam programmes that work like this.
If it is absolutely essential that you move the miles you might be able to convert ...
As far as I'm aware, you can't spread one booking across multiple loyalty programmes. I recently flew from the UK to the US and back flying out on a code-share operated by Virgin and back on Delta. This was a single ticket booked with Delta and the booking page, as I recall, only had one space for one loyalty programme. Both legs of the journey were credited ...
The Flying Blue website is a mess, but there's a section which lists all partners, including airlines and how things work with them in terms of XP and miles accrual and redemption.
In the case of Delta:
WITH DELTA AIR LINES, YOU CAN:
Gain XP on eligible flights
Earn Elite bonus Miles
Extend the overall validity of your Miles
I spoke to KLM directly, and after a few back-and-forth messages, received this:
If the flights are marketed by KLM or Air France you are able to earn Miles and XP for these flights indeed.
In this example if the flights are marketed by Virgin Atlantic and operated by KLM or Air France, you would not be able to earn Miles or XP.
Please check ...
Official site says :
Gain XP on eligible flights with Air France, KLM, Aircalin, Kenya Airways, TAROM, SkyTeam, or other airline partners except Transavia.
The number of XP you gain is based on your flight type and cabin.
For example, fly from Frankfurt to New York via Amsterdam or Paris in Economy Cabin = 15 XP
(Frankfurt to Amsterdam or Paris in Economy ...
Flying Blue is not a generous program particularly if you have the misfortune to be travelling in economy class. In the UK it is sometimes nicknamed "Flying Poo".
The main advantage is that you will have Flying Blue Gold after only thirty individual flights per year. (I assume you mean "8-10 return trips per year", if you are only doing 8 flights in total ...