If by egoism you mean Stirner's egoism, then claiming egoism will lead to capitalism is a false reading of Stirner. First i will quote Wikipedia for what capitalism is:
"Capitalism is an economic system in which trade, industry, and the means of production are largely or entirely privately owned and operated for profit.Central characteristics of capitalism include capital accumulation, competitive markets and wage labour."http://en.wikipedia.org/wiki/Capitalism
Now i will quote from Stirner's The Ego and Its Own (Cambridge version, can be found here:https://libcom.org/library/ego-its-own-max-stirner):
"...teaches me to respect the laws, to refrain from injury to state property (that is, private property), to reverence divine and earthly highness, etc...." page 199.
Stirner is clearly an anti-State thinker, and he sees private property as state property, so how could he support an economic system that is based on private property?
"The position of affairs is different in the egoistic sense. I do not step shyly back from your property, but look upon it always as my property, in which I need to 'respect' nothing. Pray do the like with what you call my property! With this view we shall most easily come to an understanding with
each other." page 220.
Sounds like a communal living.
"Proudhon might spare his prolix pathos if he said: 'There are some things that belong only to a few, and to which we others will from now on lay claim or - siege. Let us take them, because one comes to property by taking, and the property of which for the present we are still deprived came to the proprietors likewise only by taking. It can be utilized better if it is in the hands of us all
than if the few control it. Let us therefore associate ourselves for the purpose of this robbery (vol).' - Instead of this, he tries to get us to believe that society is the original possessor and the sole proprietor, of imprescriptible right; against it the so-called proprietors have become thieves (La propriete c'est Ie vol); if it now deprives of his property the present proprietor, it robs him of nothing, as it is only availing itself of its imprescriptible right. - So far one comes with the spook of
society as a moral person. On the contrary, what man can obtain belongs to him: the world belongs to me. Do you say anything else by your opposite proposition? 'The world belongs to all?' All are I
and again I, etc. But you make out of the 'all' a spook, and make it sacred, so that then the 'all' become the individual's fearful master. Then the ghost of 'right' places itself on their side." page 222.
I think this paragraph summarizes Stirner's thinking very well.
"Private property lives by grace of the law. Only in the law has it its warrant - for possession is not yet property, it becomes 'mine' only by assent of the law; it is not a fact, not un foit as Proudhon
thinks, but a fiction, a thought. This is legal property, legitimate property, guaranteed property. It is mine not through me but through the - law. " page 223
"If men reach the point of losing respect for property, every one will have property, as all slaves become free men as soon as they no longer respect the master as master. Unions will then, in this matter too, multiply the individual's means and secure his assailed property." page 229.
Can you imagine a capitalist society that its individuals do not respect for property? I think union here can be understood as a some form of communal living, but not based on a sacred as "People".
"Communism rightly revolts against the pressure that I exp.erience from individual proprietors; but stili more horrible is the might that it puts in the hands of the coliectivity." page 228.
Again, problem is making collectivity new tyrant.
And Stirner does not claim everything will work out in the end:
"It will be asked, but how then will it be when the have-nots take heart? Of what sort is the settlement to be? One might as well ask that I cast a child's nativity. vVhat a slave will do as soon as he has broken his fetters, one must - await." page 231.
"Thus these goings-on are a fight for dear lift, and, in gradation upward, for more or less of a 'good living' .
And yet, at the same time, their whole round of toil and care brings in for most only 'bitter life' and 'bitter poverty'. All the bitter painstaking for this!
Restless acquisition does not let us take breath, take a calm enjoyment we do not get the comfort of our possessions." page 238
Just the opposite of capitalist claim.
"Finally, as regards competition once more, it has a continued existence by this very means, that all do not attend to their affair and come to an understanding with each other about it. Bread e.g. is a need of all the inhabitants of a city; therefore they might easily agree on setting up a public bakery. Instead of this, they leave the furnishing of the needful to the competing bakers. Just so meat to the butchers, wine to wine-dealers, etc.
Abolishing competition is not equivalent to favoring the guild. The difference is this: In the guild baking, etc., is the affair of the guild-brothers; in competition, the affair of chance competitors; in the union, of those who require baked goods, and therefore my affair, yours, the affair of neither the guildic nor the concessionary baker, but the affair of the united.
If I do not trouble myself about my affair, I must be content with what it pleases others to vouchsafe me. To have bread is my affair, my wish and desire, and yet people leave that to the bakers and hope at most to obtain through their wrangling, their getting ahead of each other, their rivalry —in short, their competition — an advantage which one could not count on in the case of the guild-brothers who were lodged entirely and alone in the proprietorship of the baking franchise. — What every one requires, every one should also take a hand in procuring and producing; it is his affair, his property, not the property of the guildic or concessionary master." page 244.
As you can see he is against competition, and favours direct control of production means.
I think it is pretty obvious that Stirner is not a capitalist. I agree the terminology he uses can lead to this assumption. Maybe Stirner uses this terminology in purpose, to subvert it, like Saul Newman says.