Only a few sprinkler valves open and jockey pump starts,but can't keep up, so fire pump starts, but shuts down on over temp due to pump is unable to over come back flow preventer, therefore pump runs dry.
Is there a low resistance back flow preventer or other means of preventing this issue.

A fire pump shouldn't shutdown on overtemperature. Is this a VFD or a medium voltage installation?

Alan, what do you mean only a few sprinkler valves open? On the test header?
the flow in the pump can't open the pump check? I'm confused can you give somemore information please.

Alan,
Like Jim and Greg, I don't have a clear picture of the problem, but one thing that always helps if the local water provider will agree to it (unfortunately, most are blind rule followers rather than thinkers, so only a few will agree) is to place the BFP on the discharge side of the pump. I always ask, but it's not often that I get the right answer.

I'm not even sure whether you have a diesel or electric pump, but it sounds like the suction supply is weak enough so that the BFP could be causing it to fail to keep up with the sprinkler flow demand.

Can you give us a better picture of the overall situation?

If the check valve is a backflow preventer on the suction side of the pump we have experienced this. It was an airplane hanger with large pumps, low pressure city water supply and the checks on the 12" RP backflow did not open to allow flow. No flow also resulted in no water to the cooling water heat exchanger. If possible and per NFPA 20 put the backflow on the discharge side of the pump.

Talk to your backflow supplier/manufacturer and see if they think that is the issue. If yes ask them if you install a smaller backflow in parallel if they think that will help. Similar to a detector check valve. Low flows go around the trim and high flows are enough to open the check valve. There are severl backflow manufacturers and all have their flow curves on data sheets but you can also contact their tech services department for help.

If supply is a dedicated ground suction tank should just be an OS&Y in the suction pipe. No check valve.

Good point what was the water flow test at the site?

Sorry for not replying immediately due to a trip. Based on the comments I
will review the bacflow curve and discuss with the local supplier.

Thank you for you comments

Al