No you can't, but not for the reason very often stated, that "you can't stack bonuses from the same magical source", which isn't stated as RAW anywhere that I know of.
The actual reason is the following rule:
Attunement (DMG p.137)
Additionally, a creature can't attune to more than one copy of an item. For example, a creature can't attune to more than one ring of protection at a time.
So you cannot attune to more than one copy of an item, with the specific example given of two rings of protection. You only get the benefit(s) from the one you are attuned to.
This means if you have two of the same item (whatever their bonus is) and they require attunement, then you can only attune to one of them and therefore only get one of their benefits.
The incorrect statement often used as to why you can't benefit from two rings of protection (for instance) appears to comes from the assumption that the combining magic effects rule applies, but this is for spells only.
Combining Magical Effects (PHB p.206)
The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.
The belief is perhaps also a holdover from previous versions of D&D which had rules about how many rings you can wear and the combination of magical items.
DMs should be aware and careful of this, as if items that do not require attunement (for example special rings of protection) are given out to PCs, then there is no RAW that says that their bonuses do not stack if two were worn by the same creature. I've looked through the magic items in the DMG and it looks as if the designers have been very careful in this regard to ensure that you can't get stacked bonuses in this way due to what must be attuned to.
It's possible that the boots are roomy enough to accommodate the slippers (especially since they are size magic), but (using common sense) I suspect that the slippers may not function unless they contact the surface to be climbed. They seem to operate by grip given that they don't work on ice, etc.
If not "grip" by ordinary friction, it is by some interaction with the surface they are in contact with, (and they seem to grant the wearer some immunity to the effects of gravity), slippers in contact with the inside of the boots seem unlikely to allow the boots to walk on vertical and overhanging surfaces.
While wearing both reduces the time taken to change from running to climbing mode, it would not eliminate it, nor would it allow running on the ceiling.
However it could be argued that the slippers grip the inside of the boots making it hard to remove the boots!
Best Answer
You may equip as many magic items as you can properly wear, only three of which can be requiring attunement.
Many magic items require attunement, which is a process that lets a specific character make use of the item's magic abilities; non-attuned items only provide their non-magical benefits. Your character may only be attuned to three items at any given time. For details, see "Attunement" on pages 136-138 of the Dungeon Master's Guide
In addition to the three attunement slots, you may use as many items not requiring attunement as you can wear.
The other half of your question is answered on pages 140-141 of the Dungeon Master's Guide, under "Wearing Magical Items": items must be worn as intended. For example, a cloak must be properly over the shoulders, boots and gloves must be worn in matched pairs, a pair of gloves cannot be worn over another pair of gloves, etc.