This script is just an example of using the ArcGIS REST API, but if you know the URL, you can easily adapt it.

# starting record offset
offset=0
# max record count
count=2000
 
# URL for the NFHL ArcGIS REST API
url="https://hazards.fema.gov/arcgis/rest/services/FIRMette/NFHLREST_FIRMette/MapServer/1/query?where=1%3D1&text=&objectIds=&time=&geometry=&geometryType=esriGeometryEnvelope&inSR=&spatialRel=esriSpatialRelIntersects&distance=&units=esriSRUnit_Foot&relationParam=&outFields=*&returnGeometry=true&returnTrueCurves=false&maxAllowableOffset=&geometryPrecision=&outSR=&havingClause=&returnIdsOnly=false&returnCountOnly=false&orderByFields=OBJECTID&groupByFieldsForStatistics=&outStatistics=&returnZ=false&returnM=false&gdbVersion=&historicMoment=&returnDistinctValues=false&resultOffset=---OFFSET---&resultRecordCount=$count&returnExtentOnly=false&datumTransformation=&parameterValues=&rangeValues=&quantizationParameters=&featureEncoding=esriDefault&f=geojson"
 
# infinite while loop; : mean true, so while : means while true, which means forever;
# you'll have to manually break out of this infinite loop
while :; do
        # generate a filename
        fn=firm_panels_$offset.json
        [ -f $fn ] || wget -O $fn "$(echo "$url" | sed "s/---OFFSET---/$offset/")"
	# read wget error
        err=$?
	# if there was a wget error or the filesize is zero
        if [ $err -ne 0 -o ! -s $fn ]; then
		# print the wget error
                [ $err -ne 0 ] && echo "$fn: wget error $err"
		# delete broken file
                rm -f $fn
		# try it again
                continue
        fi
	# we will only stop when we reached the last record
        grep -q "exceededTransferLimit.*true" $fn || break
	# move to the next offset
        offset=$(expr $offset + $count)
done