You can buy flux pens - they are great!
Air soldering iron is the ideal if you can get one.
Otherwise place your tip on those holes to pre-heat them. Then flux (if you have).
Also you could try filing a piece of solder very thin to poke through with the wire, now you solder and it should break off, but one end hopefully will solder on, and you do the other side the same, as best you can. Do the side that has less room first, then you'll know if the solder is good before finishing the good side.
One more trick you might try. When your iron is cool wind a clean strong bit of copper or stainless steel wire (paper clip) around the tip of the iron. You may want to double back over, winding in opposite direction with one wire end for extra grip. And one end of this is straight out from your iron tip up to 20mm. Then you can really get into those tight places.
Soldering if the most difficult temperamental tedious thing I've ever done in my entire life (with a standard iron).
But cleaning the end of your iron with steel wool, and I always have a heavily soaked kitchen sponge on hand, lightly pressing the iron tip on to help keep it clean as I work (this will cool the end a bit, so you might have to wait a moment for full heat to return).
You may notice a black scale come off and the copper tip revealed, this is good.