First, you should see if you can find FEMA maps of your area. Search here: https://msc.fema.gov/portal
+ 1 to this. Look at the FIRM (flood insurance rate map) for your area and figure out what your BFE (base flood elevation) and rate zone are. Add them together (if your rate zone has a number in it) and that should be the minimum elevation of your house (including basement) in order to be at market rates for flood insurance.
Judging from your recent increases, you probably had a subsidized policy before and recent changes to the NFIP (national flood insurance program) are getting rid of subsidies and bringing everyone to paying market rates.
Because most flood policies are underwritten by the NFIP, changing companies shouldn't change the premiums, though you could probably decrease coverage somewhat and decrease your premiums that way. You'd want to check with your mortgage holder before doing so as you probably have minimum coverage requirements outlined in those documents.
Also, one other thing you could look into is seeing if your community participates in the CRS (community rating system). It's a way for local governments to take community action on flood prevention (things like education, flood mitigation construction techniques - there's a whole list). The more boxes your community checks off on the CRS list, the bigger the discount on the flood insurance policies for all of the property owners in that area. We get 30% off one of our policies and 40% off of another due to their localities participation in the CRS to varying degrees. Look up if your community participates and if it doesn't, call your city/town/county manager and ask why!
I actually wrote this post on flood insurance about a year and a half ago and it's got more detail on how to look up maps and the CRS. Some of the info on the Biggert Waters Flood Act may be out of date since last I knew they were trying to push through changes to it.
http://www.plantingourpennies.com/flood-insurance-changes-part-1/