How close can I put a fridge-freezer to a gas boiler?
It really depends on where the condensing coils are for the fridge. And how hot the boiler gets. 
On the fridge the coils used to always be on the back exterior .I have one fridge they are under the bottom of the fridge and another one that they are under the metal skin on the left side.  I figured this out when cooling it down that side got quite hot. , you really don’t want any additional heat source around the fridge it could possibly cause problems including total failure (rare) but will increase the energy usage and shorten the life of the system. 
I have had hot water heaters (some call boilers) that with a thermal blanket would have been ok  to go next to a cabinet it depends. I had 1 home with partial hydronic heating that boiler (water heater) was in a very small cabinet it was an electric model but it kept a modest addition to the house heated well (the home originally had ceiling cable heat and I was matching the no ductwork design) 
Another “flipp” house had the water heater in the kitchen I put a nice thermal blanket around it and a cabinet floor to ceiling next to it and a door , by code the cabinet had to be movable because the space was two small but when I showed the inspector the cabinet could be easily moved it passed inspection.
There are multiple possibilities here that can be done keeping heat away from the fridge away from heat is best but if the boiler is like a standard low pressure system I am used to the fridge could be close but needs air flow in any case. 
This may not be a complete answer but with the info provided may help you make your decision.