First, you can't take a tax deduction for a charitable donation unless that donation is registered with the IRS as a qualified exempt organization.
Second, a donation of personal items to a charity that you have sole control over is problematic to say the least. One issue is inurement or unjust enrichment. Is it really a donation or is it a sham designed to give you a tax deduction. You also can't take a deduction for the donation of use of an item or partial ownership. Even in the case of a larger organization where self-enrichment is not an issue, partial ownership can be. For example, the pastor of a poor church that can't afford a computer for the office can't claim a tax deduction for donating his own computer unless he transfers full ownership to the church such that the church keeps the computer even if he resigned or were fired.
An employee or volunteer for a charity can also be reimbursed for out of pocket expenses as long as the charity has an accountable plan -- that is, the only expenses that are reimbursed are those that are approved by the charity and proven by receipts. Again here the concern is self-dealing. When I was a church treasurer, and I bought supplies and donated them, I made sure that the pastor signed the approval form and the person with backup signature authority on the bank account signed the check.
If you are collecting donations from others and reimbursing yourself for expenses, you have a certain potential vulnerability that you would not have if you were a profit-making business and deducting expenses that were related to your business income.
Depending on what you mean by "my own institution" you run several tax and legal risks unless you were to bring on a larger board of directors (or at least one co-chair) and have financial matters approved by someone else.
Thats not to say that it would automatically be wrong to either claim a donation or reimburse yourself from charity funds, just that it is more risky if you are the sole authority in the institution.
