Anyone got any ideas for washing handkerchiefs

At home I usually make do with a piece of kitchen roll but like to have a proper hanky when going out, so I use them frequently.

I soak them overnight in bio liquid or powder and then they come out of the machine nice and clean even after a 30degree wash.

I use a mixture of Hankies & tissues I'm like you, very phlegmy in summer.
Soak them in washing powder solution (cool), rinse then wash them with the rest of the load is what I do.

Just put them in a bucket of Milton solution, or unbranded sterilising solution. Then I would wash In one of those net bags (mine end up in the rim) with your whites.

I read of a machine cleaning regime somewhere, involving soda crystals on a 90º wash cycle. So I do this every 3 months or so and put the hankies, as they are, in for that cycle.
2 jobs in one.
I needed to have enough hankies to see me through that long.

Back in the 1950's when I helped my Granny with the washing she had an old saucepan which was kept just for boiling handkerchiefs. She added a chunk of Sunlight soap to the water and let it simmer for an hour or two before rinsing.
I'm sure times have changed since those days, Notagranny44 but you have brought back a fond memory of post-war wash days.

I inherited my mother's preserving pan - the only thing I have ever used it for is boiling handkerchiefs!