This script is just an example of using the ArcGIS REST API to download DFIRM panel features, but if you know the URL of an ArcGIS REST service, 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