This totally “depends” on the cities and the exact dates involved.  You can find extremely cheap flights between some pairs of cities on some days.  Between other cities on other days, flying can be prohibitively expensive.  Be sure to add taxes, overweight baggage fees and the cost to get between the airports and city center on both ends of your trip to your calculation.

5 hours on a train can be boring, but IMO it’s nothing compared to the “hurry up and wait” hassle of flying.  Figure a minimum of 45 minutes to get to the airport, 2 hours check-in and security time, a 1 hour flight and 45 minutes to get out of the airport and into town.

My rules of thumb:

Train ride less than 5 hours:  take the train unless flying is much cheaper.
Train ride 5 to 7 hours:  whichever is cheaper
Train ride over 7 hours:  fly unless it’s prohibitively expensive.  2nd choice would be an overnight train.  I try to limit flights and overnight trains to a max of 2 per week.  More than that makes an exhausting trip.

Are you under 26? Some train tickets are cheaper that way.
 
I might reverse the order, if it’s possible.
 
For example, fly into Frankfurt. The following prices are for >26 people.
 
Train to either Paris or Amsterdam is 39 Euros if you get a special rate at www.bahn.de .
 
Train from Paris to London can be as cheap as 44 pounds one-way (possibly cheaper, but I think that’s the latest I’ve heard).
 
Train from Amsterdam to Paris can be a little tricky so far as getting the cheapest rate. Roundtrip can be as cheap as 70 Euros (occasionally there’s an even better special), and one-way can sometimes be as cheap as 52.50 Euros (and occasionally even a special beyond that).
 
Unless there’s an unpredictable special, you are generally best booking the train tickets right on the dot of 3 months ahead, because the cheap rates sell out quickly.
 
In short, while I probably would not to train from Frankfurt to London straight, your choice of cities is quite possible by train, and not too expensive. However, all of the cheap train tickets have the same restrictions as cheap flights – you have to take the scheduled itinerary or you lose out completely.