(Reported to House from the Committee on Veterans' Affairs with amendment, H. Rept. 99-1015 (Part I)) Veterans' Education Amendments of 1986 - Title I: Revision in Educational Assistance Programs for Veterans - Authorizes educational assistance for apprenticeship or other on-the-job training under the All-Volunteer Force Educational Assistance Program (the New GI Bill). Limits the amount of educational assistance payable in any one month where the individual pursuing the educational program fails to complete 120 hours of training. Permits an alternate pay reduction schedule for armed services members participating in the New GI Bill program. Provides that basic pay may be reduced, at the individual's option, by either $100 for each of the first 12 months the individual is entitled to such pay, or $50 for each of the first 24 months the individual is entitled to such pay. Establishes the Veterans' Administration New GI Bill Educational Assistance Fund (the Fund) in the Treasury. Provides for deposits of pay reductions of participants in the New GI Bill program into the Fund. Provides that amounts in the Fund shall be available for basic educational assistance entitlements and for refunds of contributions to the Fund. Sets forth provisions for investments by the Fund. Authorizes the Administrator of Veterans Affairs to determine and define enrollment in, pursuit of, and attendance at, any program of education by an individual enrolled in or pursuing a program of education under the New GI Bill for any period for which the individual received educational assistance under the New GI Bill. Authorizes the Administrator to withhold payment of benefits until required proof of enrollment and satisfactory pursuit of a program is received. Bars duplication of benefits to Selected Reserve members under the New GI Bill and the Selected Reserve educational program. Authorizes the pursuit of flight training under the New GI Bill. Sets forth conditions for such training. Sets forth the amount of assistance for such training. Provides for refunds to contributions under the New GI Bill. Title II: Revisions of Selected Reserve Program - Provides that educational assistance under the Selected Reserve program may only be provided for pursuit of a program of education that is approved under the New GI Bill, except that Selected Reserve program assistance may not be provided for postgraduate degree programs. Limits the amount of educational assistance payable in any one month where the individual pursuing the apprenticeship or other on-the-job training program fails to complete 120 hours of training. Authorizes the Administrator to determine and define enrollment in, pursuit of, and attendance at, any program of education by an individual enrolled in or pursuing a program of education under the Selected Reserve program for any period for which the individual receives educational assistance under the Selected Reserve program. Authorizes the Administrator to withhold payment of benefits until required proof of enrollment and satisfactory pursuit of a program is received. Authorizes the pursuit of flight training under the Selected Reserve educational program. Sets forth conditions for such training. Sets forth the amount of assistance for such training. Revises the time of completion of certain eligibility requirements for the Selected Reserve educational program.