KMA is the name of a series from Nippon Chemi-Con (totally different from Nichicon). The full part number would be EKMA350EFC220MF07D or EKMA350EC3220MF07D, depending on how the leads are formed (5mm or 2.5mm Lead-Spacing)
There is really no need to exactly match the parts when replacing capacitors: what you need to do is to take down some data like capacitance, working voltage (W.V.), lead spacing, case size, and ESR and do a parametric search using a distributor website like Mouser or Digi-Key, or a cross-site search tool like Octopart or Findchips. Some parametric searches are more accurate or more complete than others, so it pays to double check the results until you get enough experience to trust the one you're using.
For capacitors in power supplies, the ESR is frequently an important parameter, since it affects how much heat is generated by continuous charging/discharging. Choosing a low-ESR type is important, and depending on how much room there is, a higher-voltage or larger-case part may have lower ESR. You can use a higher rated voltage part than was originally spec'd, and lower may also be okay: if the rail is regulated to +12V, then a 25V rated cap is just as good as a 35V one. You can use multiple-selection or ranges in the parametric search to find an appropriate part.
Getting the right lead spacing is more important than you might think, because it enables you do plug the replacement directly into the PCB holes without having to bend the pins, which might have undesirable side effects (weakened bung seal, short circuits, mechanical problems from mounting higher than flush). In confined spaces like power supplies, the case size is also important (specified as mm of diameter x height, as in 6.3x7).