Well lets just say I puttied my windows in March using Linseed Oil Putty and on the back, it says it takes 28 days to fully harden . So, I allowed for another few weeks on top of that before painting it.
You can actually get putty in a cartridge down at your local Wilko which will harden in 24 hours though.
Stick with real linseed oil putty. It's so much better. But use real linseed oil paint. Since it is pretty much made of the same stuff as the putty the two are very compatible and will bond well. The painting can be done just as soon as the putty surface is solid enough to not distort when touched with the paintbrush - a few days. Putty is made of chalk and linseed oil. Paint is made of linseed oil, chalk and other pigments. The larger proportion of oil to solids makes the paint runnier than the putty. The putty will still set under the paint as oxygen can diffuse through the vapour permeable paint allowing the oil in the putty to polymerise.
The other advantages of linseed oil paint are that, being vapour permeable, the wood stays dry and so does not rot, the paint never flakes off, it won't need repainting for more than a decade, it give off no VOCs, brushes can be cleaned with soap and water, it's kind the the skin and it does not depend on non-renewable petroleum.
A can might look expensive at first glance, but coverage is about double that of alkyd resin paints, and the long maintenance cycle and effective wood protection makes it much cheaper in the long run.
A little Glazier trick to dry and harden linseed Putty.(always use linseed as someone else said sorry forgot your name).
A handful of bonding to 5kg tub of putty. Knock it up and willd reduce drying time,handy if you have little time.
Remember if its got a skin on it you could paint it