it's a simple matter of finding turns ratios. 150/12=12.5 so if your primary is 10 turns, your HV secondary will be 125 turns. for the grid supply 70/12=5.83, so the grid secondary will be 58 turns.
you should use 16 or 18 AWG for the primary, and 24 or 28 AWG for the secondaries. in the
[data sheet] the value for the primary is shown as 22 to 85 microhenries, so if you can get a reasonably small number of turns (10 to 20) to equal a value in that range, it should work. all you would need to do is take the number of primary turns and multiply by 12.5 and by 5,8 for your secondary turns counts. the LM2588 operates between 100 and 400khz, so you will need very fast diodes.