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Stock-Based Compensation (Narrative) (Details) (USD $)
In Millions, except Share data, unless otherwise specified
3 Months Ended 6 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2014
Dec. 31, 2013
Jun. 30, 2014
Long-Term Management Incentive Compensation Plan [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Shares approved to be issued under plan 500,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
  500,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
   
Shares issued     215,082us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
   
Performance awards earned, percentage payable as stock     60.00%flxs_PerformanceAwardsEarnedPercentagePayableAsStock
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
   
Performance awards earned, percentage payable as cash     40.00%flxs_PerformanceAwardsEarnedPercentagePayableAsCash
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
   
Cash awards payable within current liabilities $ 0.5us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
  $ 0.5us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
  $ 0.6us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
Cash awards payable within long-term liabilities 0us-gaap_DeferredCompensationSharebasedArrangementsLiabilityClassifiedNoncurrent
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
  0us-gaap_DeferredCompensationSharebasedArrangementsLiabilityClassifiedNoncurrent
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
  0.4us-gaap_DeferredCompensationSharebasedArrangementsLiabilityClassifiedNoncurrent
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
Compensation cost 0.5us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
0.4us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
0.8us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
0.6us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
 
Long-Term Management Incentive Compensation Plan [Member] | 2013-2015 [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Compensation cost     0.9us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_CreationDateAxis
= flxs_TwoThousandElevenToTwoThousandThirteenMember
/ us-gaap_PlanNameAxis
= flxs_LongTermManagementIncentiveCompensationPlanMember
   
Stock Option Plans [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Period options are excercisable     10 years    
New Long-Term Management Incentive Compensation Plan [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Shares approved to be issued under plan   700,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= flxs_NewLongTermManagementIncentiveCompensationPlanMember
  700,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= flxs_NewLongTermManagementIncentiveCompensationPlanMember
 
Compensation cost 0.1us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= flxs_NewLongTermManagementIncentiveCompensationPlanMember
  0.2us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= flxs_NewLongTermManagementIncentiveCompensationPlanMember
   
New Long-Term Management Incentive Compensation Plan [Member] | 2014-2016 [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Compensation cost     1.1us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_CreationDateAxis
= flxs_TwoThousandTwelveToTwoThousandFourteenMember
/ us-gaap_PlanNameAxis
= flxs_NewLongTermManagementIncentiveCompensationPlanMember
   
New Omnibus Stock Plan [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Shares approved to be issued under plan 700,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= flxs_NewOmnibusStockPlanMember
  700,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= flxs_NewOmnibusStockPlanMember
   
Compensation cost     $ 0.4us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_PlanNameAxis
= flxs_NewOmnibusStockPlanMember
   
Period options are excercisable     10 years    
Shares available for future grants 594,900us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= flxs_NewOmnibusStockPlanMember
  594,900us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= flxs_NewOmnibusStockPlanMember