Question: My hydronic natural gas boiler came with a Armstrong S25 circulator. I will replace the Armstrong S25 circulator with a TACO 0010-F3 IFC (the closest equivalent). The Armstrong does not have a flow check, but TACO does. Should I use the flow check in the TACO circ, or not? My system has a backflow preventer on the intake line (before it enters the boiler). Another question: Does the IFC affect water flow? Thank you for replying!

Armstrong S25 (1725 RPM; 1/12 HP; no flow check). // TACO 0010-F3 IFC (3250 RPM; 1/8 HP; Integral Flow Check)

Answer: 
A backflow preventer and a flow check do different things.

The backflow preventer prevents boiler system water from being sent into your domestic water supply, while allowing your domestic water supply to fill the boiler system. It has nothing to do with system circulation.

The flow check prevents circulating system water from flowing the wrong way when the pump is shut off - that can prevent certain types of unintended thermo-siphon heat delivery when heat is not called for, and can also prevent zones in multi-zone systems from backfeeding each other.

It probably affects water flow to some extent, but unless TACO provides data with it removed, presumably the pump data for an **integral** flow check pump is for the pump with the integral (built-in) valve in place. Point it the right direction and don't worry about it, best guess.
I see no reason for you to remove the check valve if is installed it will not hurt anything. The check valve needs a small amount of pressure to open; that will generally have a minimal effect on the pump until it is near end of life and can no longer generate the required pressure. You are actually replacing your existing with a bigger pump that has a higher GPM (flow rate) and a higher head (pressure), both will normally not hurt but can help. In essence it will deliver more BTU if the boiler can supply it.